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![chapter 8 homework answer key CCSS Math Answers](https://ccssmathanswers.com/wp-content/uploads/2020/12/cropped-CCSS-Math-Answers-Logo-343x29.png) Big Ideas Math Geometry Answers Chapter 8 SimilarityStudying & Practicing Math Geometry would be done in a fun learning process for a better understanding of the concepts. So, the best guide to prepare math in a fun learning way is our provided Big Ideas Math Geometry Answers Chapter 8 Similarity Guide. In this study guide, you will discover various exercise questions, chapter reviews, tests, chapter practices, cumulative assessment, etc. to learn all topics of chapter 8 similarity. These questions and answers are explained by the subject experts in a simple manner to make students learn so easily & score maximum marks in the exams. Big Ideas Math Book Geometry Answer Key Chapter 8 SimilarityBIM Geometry Book Solutions are available for all chapters along with Chapter 8 Similarity on our website. So, make sure to check all the chapters of Big Ideas Math Book Geometry Answer Key and learn the subject thoroughly. Based on the common core 2019 curriculum, these Big Ideas Math Geometry Answers Chapter 8 Similarity are prepared. So, students can instantly take homework help from BIM Geometry Ch 8 Similarity Answers. Simply tap on the below direct links and refer to the solutions covered in the Big Ideas Math Book Geometry Answer Key Chapter 8 Similarity Guide. - Similarity Maintaining Mathematical Proficiency – Page 415
- Similarity Mathematical Practices – Page 416
- 8.1 Similar Polygons – Page 417
- Lesson 8.1 Similar Polygons – Page (418-426)
- Exercise 8.1 Similar Polygons – Page (423-426)
- 8.2 Proving Triangle Similarity by AA – Page 427
- Lesson 8.2 Proving Triangle Similarity by AA – Page (428-432)
- Exercise 8.2 Proving Triangle Similarity by AA – Page (431-432)
- 8.1 & 8.2 Quiz – Page 434
- 8.3 Proving Triangle Similarity by SSS and SAS – Page 435
- Lesson 8.3 Proving Triangle Similarity by SSS and SAS – Page (436-444)
- Exercise 8.3 Proving Triangle Similarity by SSS and SAS – Page (441-444)
- 8.4 Proportionality Theorems – Page 445
- Lesson 8.4 Proportionality Theorems – Page (446-452)
- Exercise 8.4 Proportionality Theorems – Page (450-452)
- Similarity Chapter Review – Page (454-456)
- Similarity Chapter Test – Page 457
- Similarity Cumulative Assessment – Page (458-459)
Similarity Maintaining Mathematical ProficiencyTell whether the ratios form a proportion. Question 1. \(\frac{5}{3}, \frac{35}{21}\) Answer: Yes, the ratios \(\frac{5}{3}, \frac{35}{21}\) form a proportion. Explanation: A proportion means two ratios are equal. So, cross product of \(\frac{5}{3}, \frac{35}{21}\) is 21 x 5 = 105 = 35 x 3 Therefore, \(\frac{5}{3}, \frac{35}{21}\) form a proportion. Question 2. \(\frac{9}{24}, \frac{24}{64}\) Answer: Yes, the ratios \(\frac{9}{24}, \frac{24}{64}\) form a proportion. Explanation: If the cross product of two ratios is equal, then it forms a proportion. So, 24 x 24 = 576 = 64 x 9 Therefore, the ratios \(\frac{9}{24}, \frac{24}{64}\) form a proportion. Question 3. \(\frac{8}{56}, \frac{6}{28}\) Answer: The ratios \(\frac{8}{56}, \frac{6}{28}\) do not form a proportion. Explanation: If the cross product of two ratios is equal, then it forms a proportion. So, 56 x 6 = 336, 28 x 8 = 224 Therefore, the ratios \(\frac{8}{56}, \frac{6}{28}\) do not form a proportion. Question 4. \(\frac{18}{4}, \frac{27}{9}\) Answer: The ratios \(\frac{18}{4}, \frac{27}{9}\) do not form a proportion. Explanation: If the cross product of two ratios is equal, then it forms a proportion. So, 9 x 18 = 162, 27 x 4 = 108 Therefore, the ratios \(\frac{18}{4}, \frac{27}{9}\) do not form a proportion. Question 5. \(\frac{15}{21}, \frac{55}{77}\) Answer: The ratios \(\frac{15}{21}, \frac{55}{77}\) form a proportion. Explanation: If the cross product of two ratios is equal, then it forms a proportion. So, 15 x 77 = 1155, 55 x 21 = 1155 Therefore, the ratios \(\frac{15}{21}, \frac{55}{77}\) form a proportion. Question 6. \(\frac{26}{8}, \frac{39}{12}\) Answer: The ratios \(\frac{26}{8}, \frac{39}{12}\) form a proportion. Explanation: If the cross product of two ratios is equal, then it forms a proportion. So, 26 x 12 = 312, 39 x 8 = 312 Therefore, the ratios \(\frac{26}{8}, \frac{39}{12}\) form a proportion. Find the scale factor of the dilation. ![chapter 8 homework answer key Big Ideas Math Geometry Answers Chapter 8 Similarity 1](https://ccssmathanswers.com/wp-content/uploads/2021/02/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-1.png) Answer: k = \(\frac { 3 }{ 7 } \) Explanation: The scale factor k = \(\frac { CP’ }{ CP } \) = \(\frac { 6 }{ 14 } \) = \(\frac { 3 }{ 7 } \) ![chapter 8 homework answer key Big Ideas Math Geometry Answers Chapter 8 Similarity 2](https://ccssmathanswers.com/wp-content/uploads/2021/02/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-2.png) Answer: k = \(\frac { 3 }{ 8 } \) Explanation: The scale factor k = \(\frac { CP }{ CP’ } \) = \(\frac { 9 }{ 24 } \) = \(\frac { 3 }{ 8 } \) ![chapter 8 homework answer key Big Ideas Math Geometry Answers Chapter 8 Similarity 3](https://ccssmathanswers.com/wp-content/uploads/2021/02/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-3.png) Answer: k = \(\frac { 1 }{ 2 } \) Explanation: The scale factor k = \(\frac { MK }{ M’K’ } \) = \(\frac { 14 }{ 28 } \) = \(\frac { 1 }{ 2 } \) Question 10. ABSTRACT REASONING If ratio X and ratio Y form a proportion and ratio Y and ratio Z form a proportion, do ratio X and ratio Z form a proportion? Explain our reasoning. Answer: Yes, ratio X and ratio Z form a proportion. Explanation: If ratios are proportional means they are equal. So, ratio X and ratio Y form a proportion that means X = Y ratio Y and ratio Z form a proportion that means Y = Z From the above two equations, we can say that X = Z So, ratio X and ratio Z also form a proportion. Similarity Mathematical PracticesMonitoring Progress ![chapter 8 homework answer key Big Ideas Math Geometry Answers Chapter 8 Similarity 4](https://ccssmathanswers.com/wp-content/uploads/2021/02/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-4.png) Answer: (a) Perimeter is 32 cm, area is 48 sq cm. (b) Perimeter is 48 cm, the area is 108 sq cm. (c) Perimeter is 64 cm, the area is 192 sq cm. Explanation: The perimeter of trapezoid P = 2 + 5 + 6 + 3 = 16 cm Area of trapezoid A = \(\frac { (2 + 6)3 }{ 2 } \) = \(\frac { 3(8) }{ 2 } \) = \(\frac { 24 }{ 2 } \) = 12 sq cm (a) If scale factor k = 2, then Perimeter = kP = 2 x 16 = 32 Area = k²A = 2² x 12 = 4 x 12 = 48 (b) If scale factor k = 3, then, Perimeter = kP = 3 x 16 = 48 cm Area = k²A = 3² x 12 = 9 x 12 = 108 (c) If scale factor k = 4, then Perimeter = kP = 4 x 16 = 64 Area = k²A = 4² x 12 = 16 x 12 = 192 ![chapter 8 homework answer key Big Ideas Math Geometry Answers Chapter 8 Similarity 5](https://ccssmathanswers.com/wp-content/uploads/2021/02/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-5.png) Answer: (a) Perimeter is 28 ft, area is 32 sq ft (b) Perimeter is 42 ft, area is 72 sq ft (c) Perimeter is 7 ft, area is 2 sq ft Explanation: Perimeter of parallelogram P = 2(2 + 5) = 7 x 2 = 14 ft Area of the parallelogram = 2 x 4 = 8 sq ft (a) If scale factor k = 2, then Perimeter = kP = 2 x 14 = 28 Area = k²A = 2² x 8 = 4 x 8 = 32 (b) If scale factor k = 3, then Perimeter = kP = 3 x 14 = 42 Area = k²A = 3² x 8 = 72 (c) If scale factor k = \(\frac{1}{2}\), then Perimeter = kP = \(\frac{1}{2}\) x 14 = 7 Area = k²A = \(\frac{1}{2²}\) x 8 = \(\frac{1}{4}\) x 8 = 2 Question 3. A rectangular prism is 3 inches wide, 4 inches long, and 5 inches tall. Find the surface area and volume of the image of the prism when it is dilated by a scale factor of (a) 2, (b) 3, and (c) 4. Answer: (a) Surface area is 376 sq in, volume is 480 cubic in (b) Surface area is 846 sq in, volume is 1620 cubic in (c) Surface area is 1504 sq in, volume is 3840 cubic in Explanation: The surface area of the rectangular prism A = 2(3 x 4 + 4 x 5 + 5 x 3) = 2(12 + 20 + 15) = 2(47) = 94 in Volume of the rectangular prism V = 3 x 4 x 5 = 60 in³ (a) If the scale factor k = 2, then Surface Area = k²A = 2² x 94 = 4 x 94 = 376 sq in Volume = k³V = 2³ x 60 = 8 x 60 = 480 cubic in (b) If the scale factor k = 3, then Surface Area = k²A = 3² x 94 = 9 x 94 = 846 Volume = k³V = 3³ x 60 = 27 x 60 = 1620 (c) If the scale factor k = 4, then Surface Area = k²A = 4² x 94 = 16 x 94 = 1504 Volume = k³V = 4³ x 60 = 64 x 60 = 3840 8.1 Similar PolygonsExploration 1 Comparing Triangles after a Dilation Work with a partner: Use dynamic geometry software to draw any ∆ABC. Dilate ∆ABC to form a similar ∆A’B’C’ using an scale factor k and an center of dilation. ![chapter 8 homework answer key Big Ideas Math Geometry Answers Chapter 8 Similarity 6](https://ccssmathanswers.com/wp-content/uploads/2021/02/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-6.png) c. Repeat parts (a) and (b) for several other triangles, scale factors, and centers of dilation. Do you obtain similar results? Answer: From the newly transformed triangles in part (a) and (b), side lengths of the triangles are changed by the scale factor of k and angle measures remain the same for both of the triangles ΔABC. Exploration 2 Work with a partner: Use dynamic geometry Software to draw any ∆ABC. Dilate ∆ABC to form a similar ∆A’B’C’ using any scale factor k and any center of dilation. ![chapter 8 homework answer key Big Ideas Math Geometry Answers Chapter 8 Similarity 7](https://ccssmathanswers.com/wp-content/uploads/2021/02/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-7.png) a. Compare the perimeters of ∆A’B’C and ∆ABC. What do you observe? Answer: b. Compare the areas of ∆A’B’C’ and ∆ABC. What do you observe? Answer: c. Repeat parts (a) and (b) for several other triangles, scale factors, and centers of dilation. Do you obtain similar results? LOOKING FOR STRUCTURE To be proficient in math, you need to look closely to discern a pattern or structure. Answer: Communicate Your Answer Question 3. How are similar polygons related? Answer: if two polygons are similar means they have the same shape, corresponding angles are congruent and the ratios of lengths of their corresponding sides are equal. The common ratio is called the scale factor. Question 4. A ∆RST is dilated by a scale factor of 3 to form ∆R’S’T’. The area of ∆RST is 1 square inch. What is the area of ∆R’S’T’? Answer: Area of ∆R’S’T’ = 9 sq in Explanation: Given that, Area of ∆RST = 1 sq inch Scale factor k = 3 Area of ∆R’S’T’ = k² x Area of ∆RST = 3² x 1 = 9 x 1 = 9 Lesson 8.1 Similar Polygons![chapter 8 homework answer key Big Ideas Math Geometry Answers Chapter 8 Similarity 8](https://ccssmathanswers.com/wp-content/uploads/2021/02/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.png) Answer: The pairs of congruent angles are ∠K = ∠Q, ∠J = ∠P, ∠ L = ∠R The scale factor is \(\frac { 3 }{ 2 } \) The ratios of the corresponding side lengths in a statement of proportionality are \(\frac { PQ }{ JK } = \frac { PR }{ JL } = \frac { QR }{ LK } \) Explanation: Given that, ∆JKL ~ ∆PQR The pairs of congruent angles are ∠K = ∠Q, ∠J = ∠P, ∠ L = ∠R To find the scale factor, \(\frac { PQ }{ JK } = \frac { 9 }{ 6 } \) = \(\frac { 3 }{ 2 } \), \(\frac { PR }{ JL } = \frac { 12 }{ 8 } \) = \(\frac { 3 }{ 2 } \), \(\frac { QR }{ LK } = \frac { 6 }{ 4 } \) = \(\frac { 3 }{ 2 } \) So, the scale factor is \(\frac { 3 }{ 2 } \) ![chapter 8 homework answer key Big Ideas Math Geometry Answers Chapter 8 Similarity 9](https://ccssmathanswers.com/wp-content/uploads/2021/02/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-9.png) Answer: x = 2 Explanation: The triangles are similar, so corresponding side lengths are proportional. \(\frac { RS }{ BC } \) = \(\frac { AB }{ QR } \) \(\frac { 4 }{ x } \) = \(\frac { 12 }{ 6 } \) \(\frac { 4 }{ x } \) = 2 4 = 2x x = 2 ![chapter 8 homework answer key Big Ideas Math Geometry Answers Chapter 8 Similarity 10](https://ccssmathanswers.com/wp-content/uploads/2021/02/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-10.png) Answer: KM = 42 Explanation: Scale factor = \(\frac { JM }{ GH } \) = \(\frac { 48 }{ 40 } \) = \(\frac { 6 }{ 5 } \) Because the ratio of the lengths of the altitudes in similar triangles is equal to the scale factor, you can write the following proportion \(\frac { KM }{ HF } \) = \(\frac { 6 }{ 5 } \) \(\frac { KM }{ 35 } \) = \(\frac { 6 }{ 5 } \) KM = \(\frac { 6 }{ 5 } \) x 35 KM = 42 ![chapter 8 homework answer key Big Ideas Math Geometry Answers Chapter 8 Similarity 11](https://ccssmathanswers.com/wp-content/uploads/2021/02/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-11.png) Answer: Perimeter of Gazebo A = 46 m Explanation: Scale factor = \(\frac { AB }{ FG } \) = \(\frac { 10 }{ 15 } \) = \(\frac { 2 }{ 3 } \) So, \(\frac { AE }{ FK } \) = \(\frac { 2 }{ 3 } \) \(\frac { x }{ 18 } \) = \(\frac { 2 }{ 3 } \) x = 12 \(\frac { ED }{ KJ } \) = \(\frac { 2 }{ 3 } \) \(\frac { ED }{ 15 } \) = \(\frac { 2 }{ 3 } \) ED = 10 \(\frac { DC }{ JH } \) = \(\frac { 2 }{ 3 } \) \(\frac { DC }{ 12 } \) = \(\frac { 2 }{ 3 } \) DC = 8 \(\frac { BC }{ GH } \) = \(\frac { 2 }{ 3 } \) \(\frac { BC }{ 9 } \) = \(\frac { 2 }{ 3 } \) BC = 6 Therefore, perimeter = 6 + 8 + 10 + 12 + 10 = 46 ![chapter 8 homework answer key Big Ideas Math Geometry Answers Chapter 8 Similarity 12](https://ccssmathanswers.com/wp-content/uploads/2021/02/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-12.png) Answer: Area of LMNP = 756 m 2 Explanation: As shapes are similar, their corresponding side lengths are proportional. Scale Factor k = \(\frac { NP }{ JK } \) = \(\frac { 21 }{ 7 } \) = 3 Area of LMNP = k² x Area of GHJK = 3² x 84 = 756 m 2 ![chapter 8 homework answer key Big Ideas Math Geometry Answers Chapter 8 Similarity 13](https://ccssmathanswers.com/wp-content/uploads/2021/02/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-13.png) Answer: Both the hexagons are different. On the outer side of the hexagon, all the sides are equal. In the inside hexagon among the 6-sided 3 sides are different. ![chapter 8 homework answer key Big Ideas Math Geometry Answers Chapter 8 Similarity 14](https://ccssmathanswers.com/wp-content/uploads/2021/02/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-14.png) Answer: Both the hexagons are similar. Because all the sides of the outer hexagon are equal and all the sides of the inner hexagon are also equal. Exercise 8.1 Similar PolygonsVocabulary and Core Concept Check Question 1. COMPLETE THE SENTENCE For two figures to be similar, the corresponding angles must be ____________ . and the corresponding side lengths must be _____________ . ![chapter 8 homework answer key Big Ideas Math Geometry Answers Chapter 8 Similarity 8.1 Answ 1](https://ccssmathanswers.com/wp-content/uploads/2021/02/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.1-Answ-1.png) What is the ratio of their areas? ![chapter 8 homework answer key Big Ideas Math Geometry Answers Exercise 8.1 Similar Polygons 1](https://ccssmathanswers.com/wp-content/uploads/2021/02/Big-Ideas-Math-Geometry-Answers-Exercise-8.1-Similar-Polygons-1.png) Monitoring Progress and Modeling with Mathematics In Exercises 3 and 4, find the scale factor. Then list all pairs of congruent angles and write the ratios of the corresponding side lengths in a statement of proportionality. ![chapter 8 homework answer key Big Ideas Math Geometry Answers Chapter 8 Similarity 16](https://ccssmathanswers.com/wp-content/uploads/2021/02/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-16.png) In Exercises 5-8, the polygons are similar. Find the value of x. ![chapter 8 homework answer key Big Ideas Math Geometry Answers Chapter 8 Similarity 18](https://ccssmathanswers.com/wp-content/uploads/2021/02/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-18.png) Answer: x = 20 Explanation: \(\frac { DF }{ GJ } \) = \(\frac { DE }{ GH } \) \(\frac { 16 }{ 12 } \) = \(\frac { x }{ 15 } \) x = \(\frac { 16 x 15 }{ 12 } \) = \(\frac { 240 }{ 12 } \) x = 20 ![chapter 8 homework answer key Big Ideas Math Geometry Answers Chapter 8 Similarity 20](https://ccssmathanswers.com/wp-content/uploads/2021/02/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-20.png) Answer: x = 12 Explanation: \(\frac { PN }{ KJ } \) = \(\frac { MN }{ JH } \) \(\frac { x }{ 8 } \) = \(\frac { 9 }{ 6 } \) x = \(\frac { 9 x 8 }{ 6 } \) = \(\frac { 72 }{ 6 } \) x = 12 In Exercises 9 and 10, the black triangles are similar. Identify the type of segment shown in blue and find the value of the variab1e. ![chapter 8 homework answer key Big Ideas Math Geometry Answers Chapter 8 Similarity 22](https://ccssmathanswers.com/wp-content/uploads/2021/02/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-22.png) Explanation: \(\frac { y }{ 18 } \) = \(\frac { y – 1 }{ 16 } \) 18(y – 1) = 16y 18y – 18 = 16y 18y – 16y = 18 2y = 18 y = 9 In Exercises 11 and 12, RSTU ~ ABCD. Find the ratio of their perimeters. ![chapter 8 homework answer key Big Ideas Math Geometry Answers Chapter 8 Similarity 24](https://ccssmathanswers.com/wp-content/uploads/2021/02/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-24.png) In Exercises 13-16, two polygons are similar. The perimeter of one polygon and the ratio of the corresponding side lengths are given. Find the perimeter of the other polygon. ![chapter 8 homework answer key Big Ideas Math Geometry Answers Chapter 8 Similarity 8.1 Answ 13](https://ccssmathanswers.com/wp-content/uploads/2021/02/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.1-Answ-13.png) Question 14. perimeter of smaller polygon: 66 ft: ratio: \(\frac{3}{4}\) Answer: The perimeter of larger polygon is 88 ft. Explanation: \(\frac { smaller }{ larger } \) = \(\frac { 66 }{ x } \) = \(\frac{3}{4}\) 66 x 4 = 3x 3x = 264 x = \(\frac { 264 }{ 3 } \) = 88 ![chapter 8 homework answer key Big Ideas Math Geometry Answers Chapter 8 Similarity 8.1 Answ 15](https://ccssmathanswers.com/wp-content/uploads/2021/02/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.1-Answ-15.png) Question 16. perimeter of larger polygon: 85 m; ratio: \(\frac{2}{5}\) Answer: The perimeter of smaller polygon is 34 m. Explanation: \(\frac { smaller }{ larger } \) = \(\frac { x }{ 85 } \) = \(\frac{2}{5}\) 85 x 2 = 5x 5x = 170 x = \(\frac { 170 }{ 5 } \) = 34 ![chapter 8 homework answer key Big Ideas Math Geometry Answers Chapter 8 Similarity 8.1 Answ 17](https://ccssmathanswers.com/wp-content/uploads/2021/02/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.1-Answ-17.png) Question 18. MODELING WITH MATHEMATICS Your family has decided to put a rectangular patio in your backyard. similar to the shape of your backyard. Your backyard has a length of 45 feet and a width of 20 feet. The length of your new patio is 18 feet. Find the perimeters of your backyard and of the patio. Answer: The perimeter of the backyard is 130 ft. Perimeter of patio is 52 ft ![chapter 8 homework answer key Big Ideas Math Geometry Answers Chapter 8 1](https://ccssmathanswers.com/wp-content/uploads/2021/02/big-ideas-math-geometry-answers-chapter-8-1.png) In Exercises 19-22, the polygons are similar. The area of one polygon is given. Find the area of the other polygon. ![chapter 8 homework answer key Big Ideas Math Geometry Answers Chapter 8 Similarity 26](https://ccssmathanswers.com/wp-content/uploads/2021/02/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-26.png) Answer: Area of the larger triangle is 90 cm² Explanation: \(\frac { 10 }{ A } \) = (\(\frac { 4 }{ 12 } \))² \(\frac { 10 }{ A } \) = \(\frac { 1 }{ 9 } \) A = 10 x 9 A = 90 ![chapter 8 homework answer key Big Ideas Math Geometry Answers Chapter 8 Similarity 28](https://ccssmathanswers.com/wp-content/uploads/2021/02/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-28.png) Answer: Area of smaller triangle = 6 sq cm Explanation: \(\frac { A }{ 96 } \) = (\(\frac { 3 }{ 12 } \))² \(\frac { A }{ 96 } \) = \(\frac { 1 }{ 16 } \) 16A = 96 A = \(\frac { 96 }{ 16 } \) A = 6 ![chapter 8 homework answer key Big Ideas Math Geometry Answers Chapter 8 Similarity 30](https://ccssmathanswers.com/wp-content/uploads/2021/02/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-30.png) Answer: Because the first ratio has a side of A over the side length of B, the square of the second ratio should have the area of B over the area of A. \(\frac { 24 }{ x } \) = (\(\frac { 6 }{ 18 } \))² \(\frac { 24 }{ x } \) = \(\frac { 1 }{ 9 } \) x = 24 x 9 x = 216 In Exercises 25 and 26, decide whether the red and blue polygons are similar. ![chapter 8 homework answer key Big Ideas Math Geometry Answers Chapter 8 Similarity 32](https://ccssmathanswers.com/wp-content/uploads/2021/02/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-32.png) Answer: Yes Because both shapes are apparent and their side lengths are proportional and their corresponding angles are congruent. ![chapter 8 homework answer key Big Ideas Math Geometry Answers Chapter 8 Similarity 8.1 Answ 27](https://ccssmathanswers.com/wp-content/uploads/2021/02/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.1-Answ-27.png) ANALYZING RELATIONSHIPS In Exercises 28 – 34, JKLM ~ EFGH. ![chapter 8 homework answer key Big Ideas Math Geometry Answers Chapter 8 Similarity 45](https://ccssmathanswers.com/wp-content/uploads/2021/02/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-45.png) Question 28. Find the scale factor of JKLM to EFGH. Answer: scale factor = \(\frac { EF }{ JK } \) =\(\frac { 8 }{ 20 } \) k = \(\frac { 2 }{ 5 } \) ![chapter 8 homework answer key Big Ideas Math Geometry Answers Chapter 8 Similarity 8.1 Answ 29](https://ccssmathanswers.com/wp-content/uploads/2021/02/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.1-Answ-29.png) Question 30. Find the values of x, y, and z. Answer: x = \(\frac { 55 }{ 2 } \) y = 12 z = 65° Explanation: \(\frac { KL }{ GF } \) = \(\frac { x }{ 11 } \) = \(\frac { 5 }{ 2 } \) 2x = 55 x = \(\frac { 55 }{ 2 } \) \(\frac { MJ }{ HE } \) = \(\frac { 30 }{ y } \) = \(\frac { 5 }{ 2 } \) 5y = 60 y = 12 ![chapter 8 homework answer key Big Ideas Math Geometry Answers Chapter 8 Similarity 8.1 Answ 31](https://ccssmathanswers.com/wp-content/uploads/2021/02/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.1-Answ-31.png) Question 32. Find the ratio of the perimeters of JKLM to EFGH. Answer: The perimeter of JKLM : Perimeter of EFGH = 85 : 34 ![chapter 8 homework answer key Big Ideas Math Geometry Answers Chapter 8 Similarity 8.1 Answ 33](https://ccssmathanswers.com/wp-content/uploads/2021/02/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.1-Answ-33.png) Question 34. Find the ratio of the areas of JKLM to EFGH. Answer: Area of JKLM : Area of EFGH = 378.125 : 60.5 = 25 : 4 ![chapter 8 homework answer key Big Ideas Math Geometry Answers Chapter 8 Similarity 8.1 Answ 35](https://ccssmathanswers.com/wp-content/uploads/2021/02/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.1-Answ-35.png) Answer: The tennis table and court are not similar Explanation: If two figures are similar then their angles are congruent and sides are proportional. If the tennis court and table are similar, then \(\frac { length of table }{ length of court } \) = \(\frac { width of table }{ width of court } \) \(\frac { 9 }{ 78 } \) = \(\frac { 5 }{ 36 } \) 9 • 36 = 5 • 78 324 = 390 So, Table and court are not similar. MATHEMATICAL CONNECTIONS In Exercises 37 and 38, the two polygons are similar. Find the values of x and y. ![chapter 8 homework answer key Big Ideas Math Geometry Answers Chapter 8 Similarity 35](https://ccssmathanswers.com/wp-content/uploads/2021/02/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-35.png) Answer: x = 7.5 Explanation: \(\frac { x }{ 5 } \) = \(\frac { 6 }{ 4 } \) x = \(\frac { 15 }{ 2 } \) ATTENDING TO PRECISION In Exercises 39 – 42. the figures are similar. Find the missing corresponding side length. ![chapter 8 homework answer key Big Ideas Math Geometry Answers Chapter 8 Similarity 8.1 Answ 39](https://ccssmathanswers.com/wp-content/uploads/2021/02/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.1-Answ-39.png) Question 40. Figure A has a perimeter of 24 inches. Figure B has a perimeter of 36 inches and one of the side lengths is 12 inches. Answer: The corresponding side length of figure A is 8 in Explanation: \(\frac { Perimeter of A }{ Perimeter of B } \) = \(\frac { Side length of A }{ Side length of B } \) \(\frac { 24 }{ 36 } \) = \(\frac { x }{ 12 } \) \(\frac { 2 }{ 3 } \) = \(\frac { x }{ 12 } \) 12 • 2 = 3x x = 8 ![chapter 8 homework answer key Big Ideas Math Geometry Answers Chapter 8 Similarity 8.1 Answ 41](https://ccssmathanswers.com/wp-content/uploads/2021/02/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.1-Answ-41.png) Question 42. Figure A has an area of 18 square feet. Figure B has an area of 98 square feet and one of the side lengths is 14 feet. Answer: The corresponding side length of figure A is 6 ft. Explanation: \(\frac { Area of A }{ Area of B } \) = (\(\frac { Side length of A }{ Side length of B } \))² \(\frac { 18 }{ 98 } \) = (\(\frac { x }{ 14 } \))² \(\frac { 9 }{ 49 } \) = \(\frac { x² }{ 196 } \) x² = 36 x = 6 CRITICAL THINKING In Exercises 43-48, tell whether the polygons are always, sometimes, or never similar. ![chapter 8 homework answer key Big Ideas Math Geometry Answers Chapter 8 Similarity 8.1 Answ 43](https://ccssmathanswers.com/wp-content/uploads/2021/02/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.1-Answ-43.png) Question 44. two isosceles trapezoids Answer: Two isosceles trapezoids are sometimes similar. ![chapter 8 homework answer key Big Ideas Math Geometry Answers Chapter 8 Similarity 8.1 Answ 45](https://ccssmathanswers.com/wp-content/uploads/2021/02/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.1-Answ-45.png) Question 46. two squares Answer: Two squares are always similar. ![chapter 8 homework answer key Big Ideas Math Geometry Answers Chapter 8 Similarity 8.1 Answ 47](https://ccssmathanswers.com/wp-content/uploads/2021/02/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.1-Answ-47.png) Question 48. a right triangle and an equilateral triangle Answer: A right triangle and an equilateral triangle are never similar. ![chapter 8 homework answer key Big Ideas Math Geometry Answers Chapter 8 Similarity 8.1 Answ 49](https://ccssmathanswers.com/wp-content/uploads/2021/02/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.1-Answ-49.png) Question 52. PROVING A THEOREM Prove the Perimeters of Similar Polygons Theorem (Theorem 8.1) for similar rectangles. Include a diagram in your proof. ![chapter 8 homework answer key Big Ideas Math Geometry Answers Chapter 8 2](https://ccssmathanswers.com/wp-content/uploads/2021/02/big-ideas-math-geometry-answers-chapter-8-2.png) Question 54. THOUGHT PROVOKING The postulates and theorems in this book represent Euclidean geometry. In spherical geometry. all points are points on the surface of a sphere. A line is a circle on the sphere whose diameter is equal to the diameter of the sphere. A plane is the surface of the sphere. In spherical geometry, is it possible that two triangles are similar but not congruent? Explain your reasoning. Answer: - In Euclidean geometry, a postulate exists starting that through a point, there exists only one parallel line.
- In spherical geometry, great circles are straight lines and all of them intersect all the others. So, they are all parallel to each other. Thus, there are no parallel lines in spherical geometry.
- In spherical geometry, a line is a great circle. If there are many lines that contain any point then they are perpendicular to another line.
- So, in spherical geometry, eight right angles are formed by two perpendicular lines.
![chapter 8 homework answer key Big Ideas Math Geometry Answers Chapter 8 Similarity 39](https://ccssmathanswers.com/wp-content/uploads/2021/02/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-39.png) Maintaining Mathematical proficiency Find the value of x. ![chapter 8 homework answer key Big Ideas Math Geometry Answers Chapter 8 Similarity 41](https://ccssmathanswers.com/wp-content/uploads/2021/02/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-41.png) Answer: x = 66° Explanation: x + 24 + 90 = 180 x + 114 = 180 x = 180 – 114 x = 66 ![chapter 8 homework answer key Big Ideas Math Geometry Answers Chapter 8 Similarity 43](https://ccssmathanswers.com/wp-content/uploads/2021/02/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-43.png) Answer: x = 60° Explanation: x + x + x = 180 3x = 180 x = 60 8.2 Proving Triangle Similarity by AAComparing Triangles Work with a partner. Use dynamic geometry software. ![chapter 8 homework answer key Big Ideas Math Answers Geometry Chapter 8 Similarity 46](https://ccssmathanswers.com/wp-content/uploads/2021/02/Big-Ideas-Math-Answers-Geometry-Chapter-8-Similarity-46.png) c. Are the two triangles similar? Explain. CONSTRUCTING VIABLE ARGUMENTS To be proficient in math, you need to understand and use stated assumptions, definitions, and previously established results in constructing arguments. Answer: d. Repeat parts (a) – (c) to complete columns 2 and 3 of the table for the given angle measures. Answer: e. Complete each remaining column of the table using your own choice of two pairs of equal corresponding angle measures. Can you construct two triangles in this way that are not similar? Answer: f. Make a conjecture about any two triangles with two pairs of congruent corresponding angles. Answer: ![chapter 8 homework answer key Big Ideas Math Answers Geometry Chapter 8 Similarity 48](https://ccssmathanswers.com/wp-content/uploads/2021/02/Big-Ideas-Math-Answers-Geometry-Chapter-8-Similarity-48.png) Question 2. What can you conclude about two triangles when you know that two pairs of corresponding angles are congruent? Answer: If two pairs of corresponding angles in a pair of triangles are congruent, then the triangles are similar. Because if the two angle pairs are the same, then the third pair must also be equal when the three angle pairs are all equal, the three pairs of sides must be in proportion. Question 3. Find RS in the figure at the left. Answer: In a triangle RST TS = RS We know that TS = 4 Then RS = 4. Lesson 8.2 Proving Triangle Similarity by AAShow that the triangles are similar. Write a similarity statement. ![chapter 8 homework answer key Big Ideas Math Answers Geometry Chapter 8 Similarity 49](https://ccssmathanswers.com/wp-content/uploads/2021/02/Big-Ideas-Math-Answers-Geometry-Chapter-8-Similarity-49.png) Answer: m∠CDF + 32 = 90 degrees m∠CDF = 58 degrees ∠CDF ≅∠DFE And ∠CFE ≅ DFE So, △CDF = △DEF. ![chapter 8 homework answer key Big Ideas Math Answers Geometry Chapter 8 Similarity 51](https://ccssmathanswers.com/wp-content/uploads/2021/02/Big-Ideas-Math-Answers-Geometry-Chapter-8-Similarity-51.png) Question 4. WHAT IF? A child who is 58 inches tall is standing next to the woman in Example 3. How long is the child’s shadow’? Answer: Given that, The child is 58 inches tall and is standing next to the woman. The child shadow is 60/58 = 40/x 2330 = 60x 2330/60 = x x = 38.8. Therefore Childs shadow is 38.8 cm. Question 5. You are standing outside, and you measure the lengths 0f the shadows cast by both you and a tree. Write a proportion showing how you could find the height of the tree. Answer: The propagation shows to find the height of the tree is My height/tree height = my shadow/tree shadow. Exercise 8.2 Proving Triangle Similarity by AA![chapter 8 homework answer key Big Ideas Math Geometry Answers Chapter 8 Similarity 8.2 Answ 1](https://ccssmathanswers.com/wp-content/uploads/2021/02/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.2-Answ-1.png) Question 2. WRITING Can you assume that corresponding sides and corresponding angles of any two similar triangles are congruent? Explain. Answer: The corresponding angles of two similar triangles are always congruent but the corresponding angles of two analogous triangles are always harmonious but the corresponding sides of the two triangles don’t have to be harmonious. In an analogous triangle, the corresponding sides are commensurable which means that the rates of corresponding sides are equal. However, also the corresponding sides are harmonious, but in other cases, if these rates are 1. In Exercises 3 – 6. determine whether the triangles are similar. If they are, write a similarity statement. Explain your reasoning. ![chapter 8 homework answer key Big Ideas Math Answers Geometry Chapter 8 Similarity 52](https://ccssmathanswers.com/wp-content/uploads/2021/02/Big-Ideas-Math-Answers-Geometry-Chapter-8-Similarity-52.png) In Exercises 7 – 10. show that the two triangles are similar. ![chapter 8 homework answer key Big Ideas Math Answers Geometry Chapter 8 Similarity 56](https://ccssmathanswers.com/wp-content/uploads/2021/02/Big-Ideas-Math-Answers-Geometry-Chapter-8-Similarity-56.png) In Exercises 11 – 18, use the diagram to copy and complete the statement. ![chapter 8 homework answer key Big Ideas Math Answers Geometry Chapter 8 Similarity 60](https://ccssmathanswers.com/wp-content/uploads/2021/02/Big-Ideas-Math-Answers-Geometry-Chapter-8-Similarity-60.png) Question 12. ∆DCF ~ _________ Answer: △DCF ~ △BCG ![chapter 8 homework answer key Big Ideas Math Geometry Answers Chapter 8 Similarity 8.2 Answ 13](https://ccssmathanswers.com/wp-content/uploads/2021/02/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.2-Answ-13.png) Question 14. m∠ECF = _________ Answer: m∠ECF = 37 degrees. ![chapter 8 homework answer key Big Ideas Math Geometry Answers Chapter 8 Similarity 8.2 Answ 15](https://ccssmathanswers.com/wp-content/uploads/2021/02/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.2-Answ-15.png) Question 16. CF = _________ Answer: CF = 16 ![chapter 8 homework answer key Big Ideas Math Geometry Answers Chapter 8 Similarity 8.2 Answ 17](https://ccssmathanswers.com/wp-content/uploads/2021/02/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.2-Answ-17.png) Question 18. DE = _________ Answer: DE = 21 ![chapter 8 homework answer key Big Ideas Math Answers Geometry Chapter 8 Similarity 61](https://ccssmathanswers.com/wp-content/uploads/2021/02/Big-Ideas-Math-Answers-Geometry-Chapter-8-Similarity-61.png) To estimate the height of the pole △CDE can be proved similar to △CAD as ∠C (common angle) ∠CED = ∠CBA (corresponding angles) If two angles of one triangle are congruent to two angles of another triangle, then the two triangles are similar. △CDE ~ △CAB Corresponding angles are congruent and corresponding sides are proportional for similar triangles. DE/AB = CE/CB is an equation 1 Measure my height (DE), shadows CE and CB to calculate the height of pole (AB) from equation 1. REASONING In Exercises 23 – 26, is it possible for ∆JKL and ∆XYZ to be similar? Explain your reasoning. ![chapter 8 homework answer key Big Ideas Math Geometry Answers Chapter 8 Similarity 8.2 Answ 23](https://ccssmathanswers.com/wp-content/uploads/2021/02/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.2-Answ-23.png) Question 24. ∆JKL is a right triangle and m∠X + m∠Y= 150°. Answer: The sum of angles = 180 150 + 90 > 180 So, the answer is no. ![chapter 8 homework answer key Big Ideas Math Geometry Answers Chapter 8 Similarity 8.2 Answ 25](https://ccssmathanswers.com/wp-content/uploads/2021/02/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.2-Answ-25.png) Question 26. m∠J + m∠K = 85° and m∠Y + m∠Z = 80° Answer: The third angle in both triangles would be: For△JKL m∠L=180−85 m∠L=95 For△XYZ, m∠X=180 − 80 m∠X=100 So, there wouldn’t be any single similar angle. So, no the two triangles△JKL,△ XYZ could not be similar. ![chapter 8 homework answer key Big Ideas Math Answers Geometry Chapter 8 Similarity 64](https://ccssmathanswers.com/wp-content/uploads/2021/02/Big-Ideas-Math-Answers-Geometry-Chapter-8-Similarity-64.png) Question 30. THOUGHT PROVOKING Decide whether each is a valid method of showing that two quadrilaterals are similar. Justify your answer. a. AAA Answer: The AAA Similarity Theorem is for triangles only and therefore, cannot be applied in case of quadrilaterals. Hence the AAA system is not valid for showing two quadrilaterals to be analogous. b. AAAA Answer: The AAAA method is not a valid method for showing two quadrilaterals to be similar as in case of the rectangle and a square, all the four and the rectangle are not similar because the corresponding sides are not proportional. ![chapter 8 homework answer key Big Ideas Math Geometry Answers Chapter 8 Similarity 8.2 Answ 31](https://ccssmathanswers.com/wp-content/uploads/2021/02/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.2-Answ-31.png) Maintaining Mathematical Practices Determine whether there is enough information to prove that the triangles are congruent. Explain your reasoning. ![chapter 8 homework answer key Big Ideas Math Answers Geometry Chapter 8 Similarity 67](https://ccssmathanswers.com/wp-content/uploads/2021/02/Big-Ideas-Math-Answers-Geometry-Chapter-8-Similarity-67.png) 8.1 & 8.2 QuizList all pairs of congruent angles. Then write the ratios of the corresponding side lengths in a statement of proportionality. ![chapter 8 homework answer key Big Ideas Math Answers Geometry Chapter 8 Similarity 70](https://ccssmathanswers.com/wp-content/uploads/2021/02/Big-Ideas-Math-Answers-Geometry-Chapter-8-Similarity-70.png) The polygons are similar. Find the value of x. ![chapter 8 homework answer key Big Ideas Math Answers Geometry Chapter 8 Similarity 72](https://ccssmathanswers.com/wp-content/uploads/2021/02/Big-Ideas-Math-Answers-Geometry-Chapter-8-Similarity-72.png) Determine whether the polygons are similar. If they are, write a similarity statement. Explain your reasoning. (Section 8.1 and Section 8.2) ![chapter 8 homework answer key Big Ideas Math Answers Geometry Chapter 8 Similarity 74](https://ccssmathanswers.com/wp-content/uploads/2021/02/Big-Ideas-Math-Answers-Geometry-Chapter-8-Similarity-74.png) Show that the two triangles are similar. ![chapter 8 homework answer key Big Ideas Math Answers Geometry Chapter 8 Similarity 77](https://ccssmathanswers.com/wp-content/uploads/2021/02/Big-Ideas-Math-Answers-Geometry-Chapter-8-Similarity-77.png) Question 11. The dimensions of an official hockey rink used by the National Hockey League (NHL) are 200 feet by 85 feet. The dimensions of an air hockey table are 96 inches by 408 inches. Assume corresponding angles are congruent. (Section 8.1) a. Determine whether the two surfaces are similar. Answer: Given, The dimensions of an official hockey rink used by the National Hockey League (NHL) are 200 feet by 85 feet. The dimensions of an air hockey table are 96 inches by 408 inches. 1 feet = 12 inches 200 feet = 200 × 12 = 2400 inches 85 feet = 85 × 12 = 1020 inches Dimensions of a hockey rink in inches are 2400 inches by 1020 inches If the measure of the corresponding sides that include the angles are proportional hockey rink and hockey table are similar 200/96 = 240/96 = 25 inches 85/40.8 = 1020/10.8 = 25 inches 2400/96 = 1020/40.8 = 25 inches Thus the two rinks are similar. b. If the surfaces are similar, find the ratio of their perimeters and the ratio of their areas. If not, find the dimensions of an air hockey table that are similar to an NHL hockey rink. Answer: P1 = 2(l + w) 2(2400 + 1020) 2(3420) = 6840 inches P2 = 2(l + w) 2(96 + 40.8) 2(136.8) = 273.6 inches P1/P2 = 6840/273.6 = 25 inches A1 = lw A1 = 2400 × 1020 = 2448000 sq. inch A2 = lw A2 = 96 × 40.8 = 3916.8 sq. inch A1/A2 = 2448000/3916.8 = 625 sq. inch ![chapter 8 homework answer key Big Ideas Math Answers Geometry Chapter 8 Similarity 80](https://ccssmathanswers.com/wp-content/uploads/2021/02/Big-Ideas-Math-Answers-Geometry-Chapter-8-Similarity-80.png) 8.3 Proving Triangle Similarity by SSS and SASDeciding Whether Triangles Are Similar Work with a partner: Use dynamic geometry software. ![chapter 8 homework answer key Big Ideas Math Geometry Answer Key Chapter 8 Similarity 81](https://ccssmathanswers.com/wp-content/uploads/2021/02/Big-Ideas-Math-Geometry-Answer-Key-Chapter-8-Similarity-81.png) b. Copy the table and complete column 1. Answer: c. Are the triangles similar? Explain your reasoning. Answer: d. Repeat parts (a) – (c) for columns 2 – 6 in the table. Answer: e. How are the corresponding side lengths related in each pair of triangles that are similar? Is this true for each pair of triangles that are not similar? Answer: f. Make a conjecture about the similarity of two triangles based on their corresponding side lengths. CONSTRUCTING VIABLE ARGUMENTS To be proficient in math, you need to analyze situations by breaking them into cases and recognize and use counterexamples. Answer: g. Use your conjecture to write another set of side lengths of two similar triangles. Use the side lengths to complete column 7 of the table. Answer: Work with a partner: Use dynamic geometry software. Construct any ∆ABC. a. Find AB, AC, and m∠A. Choose any positive rational number k and construct ∆DEF so that DE = k • AB, DF = k • AC, and m∠D = m∠A. Answer: b. Is ∆DEF similar to ∆ABC? Explain your reasoning. Answer: c. Repeat parts (a) and (b) several times by changing ∆ABC and k. Describe your results. Answer: Question 3. What are two ways to use the corresponding sides of two triangles to determine that the triangles are similar? Answer: If the pairs of corresponding sides are in proportion and the included angle of each pair is equal. Then the two triangles they form are similar. Any time two sides of a triangle and their included angles are fixed. Then all three vertices of that triangle are fixed. Lesson 8.3 Proving Triangle Similarity by SSS and SASMonitoring progress Use the diagram. ![chapter 8 homework answer key Big Ideas Math Geometry Answer Key Chapter 8 Similarity 82](https://ccssmathanswers.com/wp-content/uploads/2021/02/Big-Ideas-Math-Geometry-Answer-Key-Chapter-8-Similarity-82.png) Question 1. Which of the three triangles are similar? Write a similarity statement. Answer: The ratios are equal. So, △LMN, △XYZ are similar. The ratios are not equal. So △LMN, △RST are not similar. Explanation: Compare △LMN, △XYZ by finding the ratios of corresponding side lengths Shortest sides: \(\frac { LM }{ YZ } \) = \(\frac { 20 }{ 30 } \) = \(\frac { 2 }{ 3 } \) Longest sides: \(\frac { LN }{ XY } \) = \(\frac { 26 }{ 39 } \) = \(\frac { 2 }{ 3 } \) Remaining sides: \(\frac { MN }{ ZX } \) = \(\frac { 24 }{ 36 } \) = \(\frac { 2 }{ 3 } \) The ratios are equal. So, △LMN, △XYZ are similar. Compare △LMN, △RST by finding the ratios of corresponding side lengths Shortest sides: \(\frac { LM }{ RS } \) = \(\frac { 20 }{ 24 } \) = \(\frac { 5 }{ 6 } \) Longest sides: \(\frac { LN }{ ST } \) = \(\frac { 26 }{ 33 } \) Remaining sides: \(\frac { MN }{ RT } \) = \(\frac { 24 }{ 30 } \) = \(\frac { 4 }{ 5 } \) The ratios are not equal. So △LMN, △RST are not similar. Question 2. The shortest side of a triangle similar to ∆RST is 12 units long. Find the other side 1enths of the triangle. Answer: The other side lengths of the triangle are 15 units, 16.5 units. Explanation: The shortest side of a triangle similar to ∆RST is 12 units Scale factor = \(\frac { 12 }{ 24 } \) = \(\frac { 1 }{ 2 } \) So, other sides are 33 x \(\frac { 12 }{ 2 } \) = 16.5, 30 x \(\frac { 12 }{ 2 } \) = 15. Explain how to show that the indicated triangles are similar. ![chapter 8 homework answer key Big Ideas Math Geometry Answer Key Chapter 8 Similarity 83](https://ccssmathanswers.com/wp-content/uploads/2021/02/Big-Ideas-Math-Geometry-Answer-Key-Chapter-8-Similarity-83.png) Answer: The shorter sides: \(\frac { 18 }{ 24 } \) = \(\frac { 3 }{ 4 } \) Longer sides: \(\frac { 21 }{ 28 } \) = \(\frac { 3 }{ 4 } \) The side lengths are proportional. So ∆SRT ~ ∆PNQ ![chapter 8 homework answer key Big Ideas Math Geometry Answer Key Chapter 8 Similarity 84](https://ccssmathanswers.com/wp-content/uploads/2021/02/Big-Ideas-Math-Geometry-Answer-Key-Chapter-8-Similarity-84.png) Answer: ∆XZW and ∆YZX are not proportional. Explanation: The shorter sides: \(\frac { 9 }{ 16 } \) Longer sides: \(\frac { 15 }{ 20 } \) = \(\frac { 3 }{ 4 } \) The side lengths are not proportional. So ∆XZW and ∆YZX are not proportional. Exercise 8.3 Proving Triangle Similarity by SSS and SAS![chapter 8 homework answer key Big Ideas Math Geometry Answer Key Chapter 8 Similarity 85](https://ccssmathanswers.com/wp-content/uploads/2021/02/Big-Ideas-Math-Geometry-Answer-Key-Chapter-8-Similarity-85.png) Monitoring progress and Modeling with Mathematics In Exercises 3 and 4, determine whether ∆JKL or ∆RST is similar to ∆ABC. ![chapter 8 homework answer key Big Ideas Math Geometry Answer Key Chapter 8 Similarity 87](https://ccssmathanswers.com/wp-content/uploads/2021/02/Big-Ideas-Math-Geometry-Answer-Key-Chapter-8-Similarity-87.png) In Exercises 5 and 6, find the value of x that makes ∆DEF ~ ∆XYZ. ![chapter 8 homework answer key Big Ideas Math Geometry Answer Key Chapter 8 Similarity 89](https://ccssmathanswers.com/wp-content/uploads/2021/02/Big-Ideas-Math-Geometry-Answer-Key-Chapter-8-Similarity-89.png) In Exercises 7 and 8, verify that ∆ABC ~ ∆DEF Find the scale factor of ∆ABC to ∆DEF ![chapter 8 homework answer key Big Ideas Math Geometry Answers Chapter 8 Similarity 8.3 Answ 7](https://ccssmathanswers.com/wp-content/uploads/2021/02/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.3-Answ-7.png) Question 8. ∆ABC: AB = 10, BC = 16, CA = 20 ∆DEF: DE = 25, EF = 40, FD =50 Answer: Compare △ABC and △DEF DE/AB = 25/10 = 5/2 EF/BC = 40/16 = 5/2 FD/CA = 50/20 = 5/2 All the ratios of corresponding length sides are equal. It is called a scale factor and its length is equal to 5/2. So, △ABC ~△DEF by the SSS similarity theorem. In Exercises 9 and 10. determine whether the two triangles are similar. If they are similar, write a similarity statement and find the scale factor of triangle B to triangle A. ![chapter 8 homework answer key Big Ideas Math Geometry Answer Key Chapter 8 Similarity 91](https://ccssmathanswers.com/wp-content/uploads/2021/02/Big-Ideas-Math-Geometry-Answer-Key-Chapter-8-Similarity-91.png) In Exercises 11 and 12, sketch the triangles using the given description. Then determine whether the two triangles can be similar. ![chapter 8 homework answer key Big Ideas Math Geometry Answers Chapter 8 Similarity 8.3 Answ 11](https://ccssmathanswers.com/wp-content/uploads/2021/02/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.3-Answ-11.png) Question 12. The side lengths of ∆ABC are 24, 8x, and 48, and the side lengths of ∆DEF are 15, 25, and 6x. Answer: \(\frac { AB }{ DE } \) = \(\frac { AC }{ DF } \) = \(\frac { BC }{ EF } \) \(\frac { 24 }{ 15 } \) = \(\frac { 8x }{ 25 } \) x = 5 In Exercises 13 – 16. show that the triangles are similar and write a similarity statement. Explain your reasoning. ![chapter 8 homework answer key Big Ideas Math Geometry Answer Key Chapter 8 Similarity 93](https://ccssmathanswers.com/wp-content/uploads/2021/02/Big-Ideas-Math-Geometry-Answer-Key-Chapter-8-Similarity-93.png) In Exercises 17 and 18, use ∆XYZ. ![chapter 8 homework answer key Big Ideas Math Geometry Answer Key Chapter 8 Similarity 97](https://ccssmathanswers.com/wp-content/uploads/2021/02/Big-Ideas-Math-Geometry-Answer-Key-Chapter-8-Similarity-97.png) Question 18. The longest side of a triangle similar to ∆XYZ is 39 units long. Find the other side lengths of the triangle. Answer: The longest side of a triangle similar to ∆XYZ is 39 units long. 13/39 = 12/y 13y = 39 × 12 13y = 468 y = 468/13 y = 36 13/39 = 10/y 13y = 39(10) 13y = 390 y = 390/13 y = 30 The side lengths are 30, 36 and 39. ![chapter 8 homework answer key Big Ideas Math Geometry Answer Key Chapter 8 Similarity 98](https://ccssmathanswers.com/wp-content/uploads/2021/02/Big-Ideas-Math-Geometry-Answer-Key-Chapter-8-Similarity-98.png) Question 20. MATHEMATICAL CONNECTIONS Find the value of n that makes ∆DEF ~ ∆XYZ when DE = 4, EF = 5, XY = 4(n + 1), YZ = 7n – 1, and ∠E ≅ ∠Y. Include a sketch. Answer: \(\frac { DE }{ XY } \) = \(\frac { EF }{ YZ } \) \(\frac { 4 }{ 4(n + 1) } \) = \(\frac { 5 }{ 7n – 1 } \) cross multiply the fractions 4(7n – 1) = 20(n + 1) 28n – 4 = 20n + 20 28n – 20n = 20 + 4 8n = 24 n = \(\frac { 24 }{ 8 } \) n = 3 ATTENDING TO PRECISION In Exercises 21 – 26, use the diagram to copy and complete the statement. ![chapter 8 homework answer key Big Ideas Math Geometry Answer Key Chapter 8 Similarity 99](https://ccssmathanswers.com/wp-content/uploads/2021/02/Big-Ideas-Math-Geometry-Answer-Key-Chapter-8-Similarity-99.png) Question 22. m∠NRQ = ___________ Answer: m∠NRQ = m∠NRP = 91° by the vertical congruence ![chapter 8 homework answer key Big Ideas Math Geometry Answers Chapter 8 Similarity 8.3 Answ 23](https://ccssmathanswers.com/wp-content/uploads/2021/02/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.3-Answ-23.png) Question 24. RQ = ___________ Answer: RQ = 4√3 Explanation: Using the pythogrean theorem NQ² = NR² + RQ² 8² = 4² + RQ² 64 = 16 + RQ² 64 – 16 = RQ² 48 = RQ² RQ = 4√3 ![chapter 8 homework answer key Big Ideas Math Geometry Answers Chapter 8 Similarity 8.3 Answ 25](https://ccssmathanswers.com/wp-content/uploads/2021/02/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.3-Answ-25.png) Question 26. m∠NPR = ___________ Answer: m∠NPR = 28° Explanation: m∠NPR + m∠NRP + m∠RNP = 180° m∠NPR + 91° + 61° = 180° m∠NPR + 152° = 180° m∠NPR = 180° – 152° m∠NPR = 28° ![chapter 8 homework answer key Big Ideas Math Geometry Answers Chapter 8 Similarity 8.3 Answ 27](https://ccssmathanswers.com/wp-content/uploads/2021/02/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.3-Answ-27.png) Explanation: Check the similarity of maroon and violet triangles. longest sides: \(\frac { 5 }{ 7 } \) shortest sides: \(\frac { 3 }{ 4 } \) remaining sides: \(\frac { 3 }{ 4 } \) The ratios are not equal. So those traingles are not similar. Check the similarity of blue and violet triangles. longest sides: \(\frac { 5 }{ 5.25 } \) = 1 shortest sides: \(\frac { 3 }{ 3 } \) = 1 remaining sides: \(\frac { 3 }{ 3 } \) = 1 The ratios are equal. So those traingles are similar. ![chapter 8 homework answer key Big Ideas Math Geometry Answer Key Chapter 8 Similarity 101](https://ccssmathanswers.com/wp-content/uploads/2021/02/Big-Ideas-Math-Geometry-Answer-Key-Chapter-8-Similarity-101.png) Question 30. WRITING Are any two right triangles similar? Explain. Answer: Yes, any two right triangles can be similar. If two right triangles are similar, then the ratio of their longest, smallest and remaining side lengths must be equal and their angles must be congruent. ![chapter 8 homework answer key Big Ideas Math Geometry Answer Key Chapter 8 Similarity 102](https://ccssmathanswers.com/wp-content/uploads/2021/02/Big-Ideas-Math-Geometry-Answer-Key-Chapter-8-Similarity-102.png) Answer: By observing the triangle ABC, m∠BAC = 90° Join the midpoints of the sides of the triangle. m∠DEF = 90° ![chapter 8 homework answer key Big Ideas Math Geometry Answer Key Chapter 8 Similarity 104](https://ccssmathanswers.com/wp-content/uploads/2021/02/Big-Ideas-Math-Geometry-Answer-Key-Chapter-8-Similarity-104.png) b. Write the ratio of the lengths of the second pair of corresponding legs. Answer: First find the length of AC using pythagorean theorem AC² + AB² = BC² AC² + 36 = 100 AC² = 64 AC = 8 Find the length of DF using pythagorean theorem DF² + DE² = EF² DF² + 18² = 30² DF² = 900 – 324 DF² = 576 DF= 24 c. Are these triangles similar? Does this suggest a Hypotenuse-Leg Similarity Theorem for right triangles? Explain. Answer: k = \(\frac { AC }{ DF } \) = \(\frac { 8 }{ 24 } \) = \(\frac { 1 }{ 3 } \) k = \(\frac { AB }{ DE } \) = \(\frac { 6 }{ 18 } \) = \(\frac { 1 }{ 3 } \) So, triangles are similar. ![chapter 8 homework answer key Big Ideas Math Geometry Answers Chapter 8 Similarity 8.3 Answ 35](https://ccssmathanswers.com/wp-content/uploads/2021/02/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.3-Answ-35.png) Question 38. THOUGHT PROVOKING Decide whether each is a valid method of showing that two quadrilaterals are similar. Justify your answer. a. SASA Answer: If an angle of one triangle is congruent to an angle of a second triangle and the lengths of the sides including these angles are proportional, then the triangles are similar. b. SASAS Answer: If two sides and the included angle of one triangle are equal to the corresponding sides and angle of another triangle, the triangles are congruent. c. SSSS Answer: If the corresponding side lengths of two triangles are proportional, then the triangles are similar. d. SASSS Answer: If two sides in one triangle are proportional to two sides in another triangle and the included angle in both are congruent, then those two triangles are similar. ![chapter 8 homework answer key Big Ideas Math Geometry Answers Chapter 8 Similarity 8.3 Answ 39](https://ccssmathanswers.com/wp-content/uploads/2021/02/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.3-Answ-39.png) Question 41. PROVING A THEOREM Copy and complete the paragraph proot of the second part of the Slopes of Parallel Lines Theorem (Theorern 3. 13) from page 439. Given m l = m n , l and n are nonvertical. Prove l || n You are given that m l = m n . By the definition of slope. m l = \(\frac{B C}{A C}\) and m n = \(\frac{E F}{D F}\) By ____________, \(\frac{B C}{A C}=\frac{E F}{D F}\). Rewriting this proportion yields ___________, ![chapter 8 homework answer key Big Ideas Math Geometry Answer Key Chapter 8 Similarity 107](https://ccssmathanswers.com/wp-content/uploads/2021/02/Big-Ideas-Math-Geometry-Answer-Key-Chapter-8-Similarity-107.png) Statements | Reasons | 1. m m = – 1 | 1. Given | 2. m = \(\frac{D E}{A D}\), m = \(\frac{A B}{B C}\) | 2. Definition of slope | 3. \(\frac{D E}{A D} \cdot-\frac{A B}{B C}\) = – 1 | 3. ________________________________ | 4. \(\frac{D E}{A D}=\frac{B C}{A B}\) | 4. Multiply each side of statement 3 by –\(\frac{B C}{A B}\). | 5. \(\frac{D E}{B C}\) = ____________ | 5. Rewrite proportion. | 6. ________________________________ | 6. Right Angles Congruence Theorem (Thm. 2.3) | 7. ∆ABC ~ ∆ADE | 7. ________________________________ | 8. ∠BAC ≅ ∠DAE | 8. Corresponding angles of similar figures are congruent. | 9. ∠BCA ≅ ∠CAD | 9. Alternate Interior Angles Theorem (Thm. 3.2) | 10. m∠BAC = m∠DAE, m∠BCA = m∠CAD | 10. ________________________________ | 11. m∠BAC + m∠BCA + 90° = 180° | 11. ________________________________ | 12. ________________________________ | 12. Subtraction Property of Equality | 13. m∠CAD + m∠DAE = 90° | 13. Substitution Property of Equality | 14. m∠CAE = m∠DAE + m∠CAD | 14. Angle Addition Postulate (Post. 1.4) | 15. m∠CAE = 90° | 15. ________________________________ | 16. ________________________________ | 16. Definition of perpendicular lines | Statements | Reasons | 1. m m = – 1 | 1. Given | 2. m = \(\frac{D E}{A D}\), m = \(\frac{A B}{B C}\) | 2. Definition of slope | 3. \(\frac{D E}{A D} \cdot-\frac{A B}{B C}\) = – 1 | 3. Correspomsding sides are opposite | 4. \(\frac{D E}{A D}=\frac{B C}{A B}\) | 4. Multiply each side of statement 3 by –\(\frac{B C}{A B}\). | 5. \(\frac{D E}{B C}\) = \(\frac { AB }{ AD } \) | 5. Rewrite proportion. | 6. Two right-angled triangles are said to be congruent to each other if the hypotenuse and one side of the right triangle are equal to the hypotenuse and the corresponding side of the other right-angled triangle. | 6. Right Angles Congruence Theorem (Thm. 2.3) | 7. ∆ABC ~ ∆ADE | 7. According to the side angle side theorem. | 8. ∠BAC ≅ ∠DAE | 8. Corresponding angles of similar figures are congruent. | 9. ∠BCA ≅ ∠CAD | 9. Alternate Interior Angles Theorem (Thm. 3.2) | 10. m∠BAC = m∠DAE, m∠BCA = m∠CAD | 10. Congruent angles | 11. m∠BAC + m∠BCA + 90° = 180° | 11. △ABC is a right-angled triangle | 12. m∠CAD + m∠DAE = 90° | 12. Subtraction Property of Equality | 13. m∠CAD + m∠DAE = 90° | 13. Substitution Property of Equality | 14. m∠CAE = m∠DAE + m∠CAD | 14. Angle Addition Postulate (Post. 1.4) | 15. m∠CAE = 90° | 15. Right Angle | 16. If two lines meet each other a an angle of 90°, then they are called the perpendicular lines. | 16. Definition of perpendicular lines | Find the coordinates of point P along the directed line segment AB so that AP to PB is the given ratio. ![chapter 8 homework answer key Big Ideas Math Geometry Answers Chapter 8 Similarity 8.3 Answ 43](https://ccssmathanswers.com/wp-content/uploads/2021/02/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.3-Answ-43.png) Question 44. A(- 3, – 5), B(9, – 1); 1 to 3 Answer: In order to divide the segment in the ratio 1 to 3, think of dividing the segment into 1 + 3 or 4 congruent pieces. Point P is the point that is 1/4 of the way from point A to B. Slope of AB = (-1 + 5)/(9+3) = 4/12 = 1/3 = rise/run To find the coordinates of point P, add 1/4 of the run to the x-coordinate of A and 1/4 of the rise to the y-coordinate of A. run = 1/4 × 3 = 3/4 rise = 1/4 × 1 = 1/4 ![chapter 8 homework answer key Big Ideas Math Geometry Answers Chapter 8 Similarity 8.3 Answ 45](https://ccssmathanswers.com/wp-content/uploads/2021/02/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.3-Answ-45.png) 8.4 Proportionality TheoremsDiscovering a Proportionality Relationship ![chapter 8 homework answer key Big Ideas Math Geometry Solutions Chapter 8 Similarity 109](https://ccssmathanswers.com/wp-content/uploads/2021/02/Big-Ideas-Math-Geometry-Solutions-Chapter-8-Similarity-109.png) b. Compare the ratios of AD to BD and AE to CE. Answer: c. Move \(\overline{D E}\) to other locations Parallel to \(\overline{B C}\) with endpoints on \(\overline{A B}\) and \(\overline{A C}\), and repeat part (b). Answer: d. Change ∆ABC and repeat parts (a) – (c) several times. Write a conjecture that summarizes your results. LOOKING FOR STRUCTURE To be proficient in math, you need to look closely to discern a pattern or structure. Answer: Work with a partner. Use dynamic geometry software to draw any AABC. ![chapter 8 homework answer key Big Ideas Math Geometry Solutions Chapter 8 Similarity 110](https://ccssmathanswers.com/wp-content/uploads/2021/02/Big-Ideas-Math-Geometry-Solutions-Chapter-8-Similarity-110.png) a. Bisect ∆B and plot point D at the intersection of the angle bisector and \(\overline{A C}\). Answer: b. Compare the ratios of AD to DC and BA to BC. Answer: c. Change ∆ABC and repeat parts (a) and (b) several times. Write a conjecture that summarizes your results. Answer: ![chapter 8 homework answer key Big Ideas Math Geometry Solutions Chapter 8 Similarity 111](https://ccssmathanswers.com/wp-content/uploads/2021/02/Big-Ideas-Math-Geometry-Solutions-Chapter-8-Similarity-111.png) - The proportionality relationship that exists in a triangle intersected by an angle bisector is it divides the opposite side into segments whose lengths are proportional to the lengths of the other two sides.
- The proportionality relationships that exist in a triangle by a line parallel to one side of a triangle intersects the other two sides, then divides the two sides proportionally.
Lesson 8.4 Proportionality Theorems![chapter 8 homework answer key Big Ideas Math Geometry Solutions Chapter 8 Similarity 112](https://ccssmathanswers.com/wp-content/uploads/2021/02/Big-Ideas-Math-Geometry-Solutions-Chapter-8-Similarity-112.png) Explanation: Triangle property thorem is \(\frac { XW }{ WV } \) = \(\frac { XY }{ YZ } \) \(\frac { 44 }{ 35 } \) = \(\frac { 36 }{ YZ } \) cross multiply the fractions 44 • YZ = 36 • 35 44 • YZ = 1260 YZ = \(\frac { 1260 }{ 44 } \) YZ = \(\frac { 315 }{ 11 } \) ![chapter 8 homework answer key Big Ideas Math Geometry Solutions Chapter 8 Similarity 113](https://ccssmathanswers.com/wp-content/uploads/2021/02/Big-Ideas-Math-Geometry-Solutions-Chapter-8-Similarity-113.png) Find the length of the given line segment. ![chapter 8 homework answer key Big Ideas Math Geometry Solutions Chapter 8 Similarity 114](https://ccssmathanswers.com/wp-content/uploads/2021/02/Big-Ideas-Math-Geometry-Solutions-Chapter-8-Similarity-114.png) Answer: \(\overline{B D}\) = 12 Explanation: All the angles are congruent. So, \(\overline{A B}\), \(\overline{C D}\), \(\overline{E F}\) are parallel. using the three parallel lines theorem \(\frac { BD }{ DF } \) = \(\frac { AC }{ CE } \) \(\frac { [latex]\overline{B D}\) }{ 30 } [/latex] = \(\frac { 16 }{ 40 } \) \(\overline{B D}\) = \(\frac { 16 }{ 40 } \) • 30 \(\overline{B D}\) = 12 ![chapter 8 homework answer key Big Ideas Math Geometry Solutions Chapter 8 Similarity 115](https://ccssmathanswers.com/wp-content/uploads/2021/02/Big-Ideas-Math-Geometry-Solutions-Chapter-8-Similarity-115.png) Answer: \(\overline{J M}\) = \(\frac { 96 }{ 5 } \) Explanation: All the angles are congruent. So, \(\overline{G H}\), \(\overline{J K}\), \(\overline{M N}\) are parallel. using the three parallel lines theorem \(\frac { HK }{ KN } \) = \(\frac { GJ }{ JM } \) \(\frac { 15 }{ 18 } \) = \(\frac { 16 }{ [latex]\overline{J M}\) } [/latex] Cross multiply 15 • \(\overline{J M}\) = 16 • 18 = 288 \(\overline{J M}\) = \(\frac { 288 }{ 15 } \) \(\overline{J M}\) = \(\frac { 96 }{ 5 } \) Find the value of the variable. ![chapter 8 homework answer key Big Ideas Math Geometry Solutions Chapter 8 Similarity 116](https://ccssmathanswers.com/wp-content/uploads/2021/02/Big-Ideas-Math-Geometry-Solutions-Chapter-8-Similarity-116.png) Answer: x = 28 Explanation: \(\overline{T V}\) is the angle bisector So, \(\frac { ST }{ TU } \) = \(\frac { SV }{ VU } \) \(\frac { 14 }{ x } \) = \(\frac { 24 }{ 48 } \) cross multiply 24x = 14 • 48 = 672 x = \(\frac { 672 }{ 24 } \) x = 28 ![chapter 8 homework answer key Big Ideas Math Geometry Solutions Chapter 8 Similarity 117](https://ccssmathanswers.com/wp-content/uploads/2021/02/Big-Ideas-Math-Geometry-Solutions-Chapter-8-Similarity-117.png) Answer: x = 4√2 Explanation: \(\overline{W Z}\) is the angle bisector So, \(\frac { YZ }{ ZX } \) = \(\frac { YW }{ WX } \) \(\frac { 4 }{ 4 } \) = \(\frac { 4√2 }{ x } \) cross multiply 4x = 4 • 4√2 = 16√2 x = 4√2 Exercise 8.4 Proportionality Theorems![chapter 8 homework answer key Big Ideas Math Geometry Answers Chapter 8 Similarity 8.4 Answ 1](https://ccssmathanswers.com/wp-content/uploads/2021/02/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.4-Answ-1.png) Question 2. VOCABULARY In ∆ABC, point R lies on \(\overline{B C}\) and \(\vec{A}\)R bisects ∆CAB. Write the proportionality statement for the triangle that is based on the Triangle Angle Bisector Theorem (Theorem 8.9). Answer: According to the triangle angle bisector theorem \(\frac { CR }{ BR } \) = \(\frac { AC }{ AB } \) In Exercises 3 and 4, find the length of \(\overline{A B}\) . ![chapter 8 homework answer key Big Ideas Math Geometry Solutions Chapter 8 Similarity 118](https://ccssmathanswers.com/wp-content/uploads/2021/02/Big-Ideas-Math-Geometry-Solutions-Chapter-8-Similarity-118.png) Answer: \(\frac { AE }{ ED } \) = \(\frac { AB }{ BC } \) \(\frac { 14 }{ 12 } \) = \(\frac { AB }{ 18 } \) AB = \(\frac { 14 }{ 12 } \) • 18 AB = 21 units. In Exercises 5 – 8, determine whether \(\overline{K M}\) || \(\overline{J N}\). ![chapter 8 homework answer key Big Ideas Math Geometry Solutions Chapter 8 Similarity 120](https://ccssmathanswers.com/wp-content/uploads/2021/02/Big-Ideas-Math-Geometry-Solutions-Chapter-8-Similarity-120.png) Question 10. 2 in.; 2 to 3 Answer: Construct a 2 inch segment and divide the segment into 2 + 3 or 5 congruent pieces. Point P is the point that is \(\frac { 1 }{ 5 } \) of the way from point A to point B. ![chapter 8 homework answer key Big Ideas Math Geometry Answers Chapter 8 Similarity 8.4 Answ 11](https://ccssmathanswers.com/wp-content/uploads/2021/02/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.4-Answ-11.png) Question 12. 9 cm ; 2 to 5 Answer: Construct a 9 cm segment and divide the segment into 2 + 5 or 7 congruent pieces. Point p is the point that is \(\frac { 1 }{ 7 } \) of the way from point A to point B. In Exercises 13 – 16, use the diagram to complete the proportion. ![chapter 8 homework answer key Big Ideas Math Geometry Solutions Chapter 8 Similarity 124](https://ccssmathanswers.com/wp-content/uploads/2021/02/Big-Ideas-Math-Geometry-Solutions-Chapter-8-Similarity-124.png) In Exercises 17 and 18, find the length of the indicated line segment. ![chapter 8 homework answer key Big Ideas Math Geometry Solutions Chapter 8 Similarity 129](https://ccssmathanswers.com/wp-content/uploads/2021/02/Big-Ideas-Math-Geometry-Solutions-Chapter-8-Similarity-129.png) In Exercises 19 – 22, find the value of the variable. ![chapter 8 homework answer key Big Ideas Math Geometry Solutions Chapter 8 Similarity 131](https://ccssmathanswers.com/wp-content/uploads/2021/02/Big-Ideas-Math-Geometry-Solutions-Chapter-8-Similarity-131.png) MATHEMATICAL CONNECTIONS In Exercises 25 and 26, find the value of x for which \(\overline{P Q}\) || \(\overline{R S}\). ![chapter 8 homework answer key Big Ideas Math Geometry Solutions Chapter 8 Similarity 137](https://ccssmathanswers.com/wp-content/uploads/2021/02/Big-Ideas-Math-Geometry-Solutions-Chapter-8-Similarity-137.png) Question 36. THOUGHT PROVOKING Write the converse of the Triangle Angle Bisector Theorem (Theorem 8.9). Is the converse true? Justify your answer. Answer: Stating the converse of the Triangle Angle Bisector Theorem. The converse of the Triangle Angle Bisector Theorem states that if a ray divides a side of a triangle into segments whose lengths are proportional to the lengths of the other two sides, it bisects the angle opposite to the first side. AB/AC = BD/DC Showing ΔABD and ΔCDE are similar By construction, CE ∣∣AB So ∠CED≅∠DAB And ∠ECD ≅ ∠DBA So ΔABD∼ΔCDE BD/CD = AB/CE AC = CE ∠CED≅∠DAB and ∠CAD≅∠DAB So, ∠CED≅∠DAB Hence AD is an angle bisector of ∠BAC ![chapter 8 homework answer key Big Ideas Math Geometry Answers Chapter 8 Similarity 8.4 Answ 37](https://ccssmathanswers.com/wp-content/uploads/2021/02/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.4-Answ-37.png) Maintaining Mathematical Proficiency Use the triangle. ![chapter 8 homework answer key Big Ideas Math Geometry Solutions Chapter 8 Similarity 149](https://ccssmathanswers.com/wp-content/uploads/2021/02/Big-Ideas-Math-Geometry-Solutions-Chapter-8-Similarity-149.png) Question 42. Which side is the hypotenuse? Answer: The leg c is the hypotenuse. Solve the equation. ![chapter 8 homework answer key Big Ideas Math Geometry Answers Chapter 8 Similarity 8.4 Answ 43](https://ccssmathanswers.com/wp-content/uploads/2021/02/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.4-Answ-43.png) Question 44. x 2 + 16 = 25 Answer: x² + 16 = 25 x² = 25 – 16 x² = 9 x = ∓ 3 ![chapter 8 homework answer key Big Ideas Math Geometry Answers Chapter 8 Similarity 8.4 Answ 45](https://ccssmathanswers.com/wp-content/uploads/2021/02/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-8.4-Answ-45.png) ![](//serviteca.online/777/templates/cheerup2/res/banner1.gif) Similarity ReviewFind the scale factor. Then list all pairs of congruent angles and write the ratios of the corresponding side lengths in a statement of proportionality. ![chapter 8 homework answer key Big Ideas Math Answer Key Geometry Chapter 8 Similarity 150](https://ccssmathanswers.com/wp-content/uploads/2021/02/Big-Ideas-Math-Answer-Key-Geometry-Chapter-8-Similarity-150.png) Question 3. Two similar triangles have a scale factor of 3 : 5. The altitude of the larger triangle is 24 inches. What is the altitude of the smaller triangle? Answer: Scale factor of smaller triangle to larger traingle is \(\frac { 3 }{ 5 } \) and larger traingle altitude is 24 inches Let x be the smaller triangle altitude \(\frac { altitude of smaller triangle }{ altitude of larger traingle } \) = scale factor \(\frac { x }{ 24 } \) = \(\frac { 3 }{ 5 } \) x = \(\frac { 3 }{ 5 } \) • 24 x = 14.4 Question 4. Two similar triangles have a pair of corresponding sides of length 12 meters and 8 meters. The larger triangle has a perimeter of 48 meters and an area of 180 square meters. Find the perimeter and area of the smaller triangle. Answer: Scale factor = \(\frac { 2 }{ 3 } \) perimeter of smaller triangle = 32 Area of smaller triangle = 80 Explanation: The scale factor of smaller to larger traingle = \(\frac { 8 }{ 12 } \) = \(\frac { 2 }{ 3 } \) \(\frac { perimeter of smaller triangle }{ perimeter of larger triangle } \) = scale factor\(\frac { perimeter of smaller triangle }{ 48 } \) = \(\frac { 2 }{ 3 } \) perimeter of smaller triangle = \(\frac { 2 }{ 3 } \) • 48 perimeter of smaller triangle = 32 \(\frac { Area of smaller triangle }{ Area of larger triangle } \) = (scale factor)² \(\frac { Area of smaller triangle }{ 180 } \) = ( \(\frac { 2 }{ 3 } \))² Area of smaller triangle = \(\frac { 4 }{ 9 } \) • 180 = 80 ![chapter 8 homework answer key Big Ideas Math Answer Key Geometry Chapter 8 Similarity 152](https://ccssmathanswers.com/wp-content/uploads/2021/02/Big-Ideas-Math-Answer-Key-Geometry-Chapter-8-Similarity-152.png) Question 7. A cellular telephone tower casts a shadow that is 72 feet long, while a nearby tree that is 27 feet tall casts a shadow that is 6 feet long. How tall is the tower? Answer: \(\frac { shadow of tree }{ shadow of tower } \) = \(\frac { height of tree }{ height of tower } \) \(\frac { 6 }{ 72 } \) = \(\frac { 27 }{ x } \) 6x = 1944 x = 324 ft The height of the tower is 324 ft. Use the SSS Similarity Theorem (Theorem 8.4) or the SAS Similarity Theorem (Theorem 8.5) to show that the triangles are similar. ![chapter 8 homework answer key Big Ideas Math Answer Key Geometry Chapter 8 Similarity 154](https://ccssmathanswers.com/wp-content/uploads/2021/02/Big-Ideas-Math-Answer-Key-Geometry-Chapter-8-Similarity-154.png) Answer: \(\frac { 24 }{ 6 } \) = 4 \(\frac { 32 }{ 2x } \) = 4 32 = 8x x = \(\frac { 32 }{ 8 } \) x = 4 Determine whether \(\overline{A B}\) || \(\overline{C D}\) ![chapter 8 homework answer key Big Ideas Math Answer Key Geometry Chapter 8 Similarity 157](https://ccssmathanswers.com/wp-content/uploads/2021/02/Big-Ideas-Math-Answer-Key-Geometry-Chapter-8-Similarity-157.png) Answer: \(\frac { DB }{ BE } \) = \(\frac { 10 }{ 16 } \) = \(\frac { 5 }{ 8 } \) \(\frac { CA }{ AE } \) = \(\frac { 20 }{ 28 } \) = \(\frac { 5 }{ 7 } \) \(\frac { DB }{ BE } \) ≠ \(\frac { CA }{ AE } \) So, CD and AB are not parallel. ![chapter 8 homework answer key Big Ideas Math Answer Key Geometry Chapter 8 Similarity 158](https://ccssmathanswers.com/wp-content/uploads/2021/02/Big-Ideas-Math-Answer-Key-Geometry-Chapter-8-Similarity-158.png) Answer: \(\frac { DB }{ BE } \) = \(\frac { 12 }{ 20 } \) = \(\frac { 3 }{ 5 } \) \(\frac { CA }{ AE } \) = \(\frac { 13.5 }{ 22.5 } \) = \(\frac { 3 }{ 5 } \) \(\frac { DB }{ BE } \) = \(\frac { CA }{ AE } \) So, AB and CD are parallel. ![chapter 8 homework answer key Big Ideas Math Answer Key Geometry Chapter 8 Similarity 159](https://ccssmathanswers.com/wp-content/uploads/2021/02/Big-Ideas-Math-Answer-Key-Geometry-Chapter-8-Similarity-159.png) Answer: \(\frac { ZC }{ AZ } \) = \(\frac { 24 }{ 15 } \) = \(\frac { 8 }{ 5 } \) \(\frac { YB }{ AY } \) = \(\frac { ZC }{ AZ } \) \(\frac { YB }{ 7 } \) = \(\frac { 8 }{ 5 } \) YB = \(\frac { 8 }{ 5 } \) • 7 YB = \(\frac { 56 }{ 5 } \) The length of \(\overline{Y B}\) is \(\frac { 56 }{ 5 } \) Find the length of \(\overline{A B}\). ![chapter 8 homework answer key Big Ideas Math Answer Key Geometry Chapter 8 Similarity 160](https://ccssmathanswers.com/wp-content/uploads/2021/02/Big-Ideas-Math-Answer-Key-Geometry-Chapter-8-Similarity-160.png) Answer: \(\frac { AB }{ 7 } \) = \(\frac { 6 }{ 4 } \) \(\overline{A B}\) = \(\frac { 6 }{ 4 } \) • 7 \(\overline{A B}\) = \(\frac { 42 }{ 4 } \) \(\overline{A B}\) = \(\frac { 21 }{ 2 } \) The length of \(\overline{A B}\) is \(\frac { 21 }{ 2 } \). ![chapter 8 homework answer key Big Ideas Math Answer Key Geometry Chapter 8 Similarity 161](https://ccssmathanswers.com/wp-content/uploads/2021/02/Big-Ideas-Math-Answer-Key-Geometry-Chapter-8-Similarity-161.png) Answer: \(\frac { DB }{ CD } \) = \(\frac { AB }{ AC } \) \(\frac { 4 }{ 10 } \) = \(\frac { AB }{ 18 } \) \(\frac { 2 }{ 5 } \) = \(\frac { AB }{ 18 } \) AB = \(\frac { 36 }{ 5 } \) Similarity TestDetermine whether the triangles are similar. If they are, write a similarity statement. Explain your reasoning. ![chapter 8 homework answer key Big Ideas Math Answer Key Geometry Chapter 8 Similarity 162](https://ccssmathanswers.com/wp-content/uploads/2021/02/Big-Ideas-Math-Answer-Key-Geometry-Chapter-8-Similarity-162.png) Answer: Longer sides: \(\frac { 32 }{ 24 } \) = \(\frac { 4 }{ 3 } \) shorter sides: \(\frac { 18 }{ 14 } \) = \(\frac { 9 }{ 7 } \) remaining sides: \(\frac { 20 }{ 15 } \) = \(\frac { 4 }{ 3 } \) Those are not equal. So, triangles are not similar. ![chapter 8 homework answer key Big Ideas Math Answer Key Geometry Chapter 8 Similarity 163](https://ccssmathanswers.com/wp-content/uploads/2021/02/Big-Ideas-Math-Answer-Key-Geometry-Chapter-8-Similarity-163.png) Answer: \(\frac { AC }{ KJ } \) = \(\frac { 6 }{ 8 } \) = \(\frac { 3 }{ 4 } \) \(\frac { BC }{ JL } \) = \(\frac { 8 }{ [latex]\frac { 32 }{ 3 } \) } [/latex] = \(\frac { 3 }{ 4 } \) \(\frac { AC }{ KJ } \) = \(\frac { BC }{ JL } \) ∠C = ∠J So, △ABC and △JLK are similar. ![chapter 8 homework answer key Big Ideas Math Answer Key Geometry Chapter 8 Similarity 164](https://ccssmathanswers.com/wp-content/uploads/2021/02/Big-Ideas-Math-Answer-Key-Geometry-Chapter-8-Similarity-164.png) Answer: \(\frac { XY }{ XW } \) = \(\frac { PZ }{ PW } \) ![chapter 8 homework answer key Big Ideas Math Answer Key Geometry Chapter 8 Similarity 165](https://ccssmathanswers.com/wp-content/uploads/2021/02/Big-Ideas-Math-Answer-Key-Geometry-Chapter-8-Similarity-165.png) Answer: \(\frac { 9 }{ w } \) = \(\frac { 15 }{ 5 } \) \(\frac { 9 }{ w } \) = 3 9 = 3w w = 3 ![chapter 8 homework answer key Big Ideas Math Answer Key Geometry Chapter 8 Similarity 166](https://ccssmathanswers.com/wp-content/uploads/2021/02/Big-Ideas-Math-Answer-Key-Geometry-Chapter-8-Similarity-166.png) Answer: \(\frac { 17.5 }{ 21 } \) = \(\frac { q }{ 33 } \) q = \(\frac { 17.5 }{ 21 } \) • 33 q = \(\frac { 55 }{ 2 } \) ![chapter 8 homework answer key Big Ideas Math Answer Key Geometry Chapter 8 Similarity 167](https://ccssmathanswers.com/wp-content/uploads/2021/02/Big-Ideas-Math-Answer-Key-Geometry-Chapter-8-Similarity-167.png) Answer: \(\frac { 21 – p }{ p } \) = \(\frac { 12 }{ 24 } \) \(\frac { 21 – p }{ p } \) = \(\frac { 1 }{ 2 } \) cross multiply 2(21 – p) = p 42 – 2p = p 42 = p + 2p 42 = 3p p = 14 Question 7. Given ∆QRS ~ ∆MNP, list all pairs of congruent angles, Then write the ratios of the corresponding side lengths in a statement of proportionality. Answer: The pairs of congruent anglres are m∠QRS, m∠RSQ, m∠SQR, m∠MNP, m∠NPM, m∠PMN. The ratios of side lengths are \(\frac { RQ }{ MN } \), \(\frac { QS }{ MP } \), \(\frac { RS }{ NP } \) ![chapter 8 homework answer key Big Ideas Math Answer Key Geometry Chapter 8 Similarity 168](https://ccssmathanswers.com/wp-content/uploads/2021/02/Big-Ideas-Math-Answer-Key-Geometry-Chapter-8-Similarity-168.png) Question 8. Find the length of \(\overline{E F}\). Answer: \(\frac { DE }{ EF } \) = \(\frac { CD }{ BC } \) \(\frac { 3.2 }{ EF } \) = \(\frac { 2.8 }{ 1.4 } \) EF = 1.6 The length of \(\overline{E F}\) is 1.6 Question 9. Find the length of \(\overline{F G}\). Answer: \(\frac { EF }{ FG } \) = \(\frac { BC }{ AB } \) \(\frac { 1.6 }{ FG } \) = \(\frac { 1.4 }{ 4.2 } \) FG = 4.8 The length of \(\overline{F G}\) is 4.8 Question 10. Is quadrilateral FECB similar to quadrilateral GFBA? If so, what is the scale factor of the dilation that maps quadrilateral FECB to quadrilateral GFBA? Answer: The scale factor of dilation from quadrilateral FECB to quadrilateral GFBA is \(\frac { GF }{ FE } \) Question 11. You are visiting the Unisphere at Flushing Meadows Corona Park in New York. To estimate the height of the stainless steel model of Earth. you place a mirror on the ground and stand where you can see the top of the model in the mirror. Use the diagram to estimate the height of the model. Explain why this method works. Answer: We know that the corresponding sides of a similar triangle are proportional height of Unisphere/distance of Unisphere from mirror = height of person/distance of the person from mirror x/100 = 5.6/4 x = 5.6 × 100/4 x = 140 Thus the estimated height of the tree = 140 ft ![chapter 8 homework answer key Big Ideas Math Answer Key Geometry Chapter 8 Similarity 169](https://ccssmathanswers.com/wp-content/uploads/2021/02/Big-Ideas-Math-Answer-Key-Geometry-Chapter-8-Similarity-169.png) Answer: we know that 1 yard = ft As per the similarity theorem \(\frac { AD }{ EH } \) = \(\frac { AB }{ EF } \) \(\frac { 2 }{ 800.3 } \) = \(\frac { 1.4 }{ EF } \) EF = 1200 • 1 • 4 EF = 1680 Perimete of the park P = 2(1680 + 2400) = 2(4080) = 8160 ft Area of the actual park = 1680 • 2400 = 4,032,000 sq ft Therefore, perimeter of the actual park = 8160 ft area of the actual park is 4,032,000 sq ft. ![chapter 8 homework answer key Big Ideas Math Answer Key Geometry Chapter 8 Similarity 170](https://ccssmathanswers.com/wp-content/uploads/2021/02/Big-Ideas-Math-Answer-Key-Geometry-Chapter-8-Similarity-170.png) Similarity Cumulative Assessment![chapter 8 homework answer key Big Ideas Math Geometry Answers Chapter 8 Similarity 171](https://ccssmathanswers.com/wp-content/uploads/2021/02/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-171.png) b. Are the quadrilaterals similar? Explain your reasoning. Answer: No. \(\frac { AD }{ QT } \) = \(\frac { 2 }{ 1.5 } \) \(\frac { CD }{ TS } \) = \(\frac { 2.8 }{ 1.4 } \) = 2 So, quadrilaterals are not similar. ![chapter 8 homework answer key Big Ideas Math Geometry Answers Chapter 8 Similarity 172](https://ccssmathanswers.com/wp-content/uploads/2021/02/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-172.png) SSS Congruence Theorem (Theorem 5.8) Answer: If all the three sides of one triangle are equivalent to the corresponding three sides of the second triangle, then the two triangles are said to be congruent by SSS rule. HL Congruence Theorem (Theorem 5.9) Answer: A given set of triangles are congruent if the corresponding lengths of their hypotenuse and one leg are equal. ASA Congruence Theorem (Theorem 5. 10) Answer: If any two angles and the side included between the angles of one triangle are equivalent to the corresponding two angles and side included between the angles of the second triangle, then the two triangles are said to be congruent by ASA rule AAS Congruence Theorem (Theorem 5. 11) Answer: AAS stands for Angle-angle-side. When two angles and a non-included side of a triangle are equal to the corresponding angles and sides of another triangle, then the triangles are said to be congruent. ![chapter 8 homework answer key Big Ideas Math Geometry Answers Chapter 8 Similarity 173](https://ccssmathanswers.com/wp-content/uploads/2021/02/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-173.png) Question 4. The slope of line l is – \(\frac{3}{4}\). The slope of line n is \(\frac{4}{3}\) What must be true about lines l and n ? (A) Lines l and n are parallel. (B) Lines l and n arc perpendicular. (C) Lines l and n are skew. (D) Lines l and n are the same line. Answer: The slope of l = – \(\frac{3}{4}\) Slope of n = \(\frac{4}{3}\) lines slopes are reciprocal and opposite. So, they are perpendicular. ![chapter 8 homework answer key Big Ideas Math Geometry Answers Chapter 8 Similarity 174](https://ccssmathanswers.com/wp-content/uploads/2021/02/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-174.png) Statements | Reasons | 1. \(\frac{K J}{K L}=\frac{K H}{K M}\) | 1. Given | 2. ∠JKH ≅ ∠LKM | 2. ________________________ | 3. ∆JKH ~ ∆LKM | 3. ________________________ | 4. ∠KHJ ≅∠KML | 4. ________________________ | 5. _______________________ | 5. Definition of congruent angles | 6. m∠KHJ + m∠JHG = 180° | 6. Linear Pair Postulate (Post. 18) | 7. m∠JHG = 180° – m∠KHJ | 7. ________________________ | 8. m∠KML + m∠LMN = 180° | 8. ________________________ | 9. ________________________ | 9. Subtraction Property of Equality | 10. m∠LMN = 180° – m∠KHJ | 10. ________________________ | 11. ________________________ | 11. Transitive Property of Equality | 12. ∠LMN ≅ ∠JHG | 12. ________________________ | Statements | Reasons | 1. \(\frac{K J}{K L}=\frac{K H}{K M}\) | 1. Given | 2. ∠JKH ≅ ∠LKM | 2. Opposite angles | 3. ∆JKH ~ ∆LKM | 3. By SSS rule if two side lengths of two triangles are proportional then triangles are similar. | 4. ∠KHJ ≅∠KML | 4. Alternate interior angles | 5. Congruent angles are angles with the exactly the same measure | 5. Definition of congruent angles | 6. m∠KHJ + m∠JHG = 180° | 6. Linear Pair Postulate (Post. 18) | 7. m∠JHG = 180° – m∠KHJ | 7. Subtraction Property of Equality | 8. m∠KML + m∠LMN = 180° | 8. Linear Pair Postulate | 9. m∠LMN + m∠KML – m∠KML = 180 – m∠KML | 9. Subtraction Property of Equality | 10. m∠LMN = 180° – m∠KHJ | 10. Transitive property of equuality | 11. m∠JHG = 180 – m∠KML | 11. Transitive Property of Equality | 12. ∠LMN ≅ ∠JHG | 12. Transitive property of equality | Question 6. The coordinates of the vertices of ∆DEF are D(- 8, 5), E(- 5, 8), and F(- 1, 4), The coordinates of the vertices of ∆JKL are J(16, – 10), K(10, – 16), and L(2, – 8), ∠D ≅ ∠J. Can you show that ∆DEF ∆JKL by using the AA Similarity Theorem (Theorem 8.3)? If so, do so by listing the congruent corresponding angles and writing a similarity transformation that maps ∆DEF to ∆JKL. If not, explain why not. Answer: AA similarity theorem states that ∠D = ∠J. So, ∆DEF and ∆JKL are similar. ![chapter 8 homework answer key Big Ideas Math Geometry Answers Chapter 8 Similarity 175](https://ccssmathanswers.com/wp-content/uploads/2021/02/Big-Ideas-Math-Geometry-Answers-Chapter-8-Similarity-175.png) Question 8. ‘Your friend makes the statement “Quadrilateral PQRS is similar to quadrilateral WXYZ.” Describe the relationships between corresponding angles and between corresponding sides that make this statement true. Answer: When 2 figures are similar, then their corresponding angles are congruent and their corresponding lengths are proportional. hence if PQRS is similar to wxyZ, then the following statements are true. ∠P = ∠W, ∠Q = ∠X, ∠R = ∠Y and ∠S = ∠Z and \(\frac { PQ }{ WX } \) = \(\frac { QR }{ XY } \) = \(\frac { RS }{ YZ } \) = \(\frac { PS }{ WZ } \) = k Here is a constant of proportionality. Leave a Comment Cancel ReplyYou must be logged in to post a comment. - Texas Go Math
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Free Download Go Math Answer Key from Kindergarten to 8th GradeStudents can find Go Math Answer Keys right from Primary School to High School all in one place. You just need to tap on the quick links available in order to access them and learn all the Chapters in each grade. Once you tap on the quick link you will be directed to the respective Grade Solutions Key wherein you can access the complete information. You can find Solutions for all the Go Math Textbook Questions free of cost and we don’t charge any amount. - Go Math Kindergarten Answer Key
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Go Math Grade K Answer Key- Chapter 1 Represent, Count, and Write Numbers 0 to 5
- Chapter 2 Compare Numbers to 5
- Chapter 3 Represent, Count, and Write Numbers 6 to 9
- Chapter 4 Represent and Compare Numbers to 10
- Chapter 5 Addition
- Chapter 6 Subtraction
- Chapter 7 Represent, Count, and Write 11 to 19
- Chapter 8 Represent, Count, and Write 20 and Beyond
- Chapter 9 Identify and Describe Two-Dimensional Shapes
- Chapter 10 Identify and Describe Three-Dimensional Shapes
- Chapter 11 Measurement
- Chapter 12 Classify and Sort Data
- Chapter 1 Addition Concepts
- Chapter 2 Subtraction Concepts
- Chapter 3 Addition Strategies
- Chapter 4 Subtraction Strategies
- Chapter 5 Addition and Subtraction Relationships
- Chapter 6 Count and Model Numbers
- Chapter 7 Compare Numbers
- Chapter 8 Two-Digit Addition and Subtraction
- Chapter 9 Measurement
- Chapter 10 Represent Data
- Chapter 11 Three-Dimensional Geometry
- Chapter 12 Two-Dimensional Geometry
- Chapter 1 Number Concepts
- Chapter 2 Numbers to 1,000
- Chapter 3 Basic Facts and Relationships
- Chapter 4 2-Digit Addition
- Chapter 5 2-Digit Subtraction
- Chapter 6 3-Digit Addition and Subtraction
- Chapter 7 Money and Time
- Chapter 8 Length in Customary Units
- Chapter 9 Length in Metric Units
- Chapter 10 Data
- Chapter 11 Geometry and Fraction Concepts
Grade 3 HMH Go Math – Answer Keys - Chapter 1: Addition and Subtraction within 1,000
- Chapter 2: Represent and Interpret Data
- Chapter 3: Understand Multiplication
- Chapter 4: Multiplication Facts and Strategies
- Chapter 5: Use Multiplication Facts
- Chapter 6: Understand Division
- Chapter 7: Division Facts and Strategies
- Chapter 8: Understand Fractions
- Chapter 9: Compare Fractions
- Chapter 10: Time, Length, Liquid Volume, and Mass
- Chapter 11: Perimeter and Area
- Chapter 12:Two-Dimensional Shapes
Grade 3 HMH Go Math – Extra Practice Questions and Answers- Chapter 1: Addition and Subtraction within 1,000 Extra Practice
- Chapter 2: Represent and Interpret Data Extra Practice
- Chapter 3: Understand Multiplication Extra Practice
- Chapter 4: Multiplication Facts and Strategies Extra Practice
- Chapter 5: Use Multiplication Facts Extra Practice
- Chapter 6: Understand Division Extra Practice
- Chapter 7: Division Facts and Strategies Extra Practice
- Chapter 8: Understand Fractions Extra Practice
- Chapter 9: Compare Fractions Extra Practice
- Chapter 10: Time, Length, Liquid Volume, and Mass Extra Practice
- Chapter 11: Perimeter and Area Extra Practice
- Chapter 12: Two-Dimensional Shapes Extra Practice
Common Core Grade 4 HMH Go Math – Answer Keys - Chapter 1 Place Value, Addition, and Subtraction to One Million
- Chapter 2 Multiply by 1-Digit Numbers
- Chapter 3 Multiply 2-Digit Numbers
- Chapter 4 Divide by 1-Digit Numbers
- Chapter 5 Factors, Multiples, and Patterns
- Chapter 6 Fraction Equivalence and Comparison
- Chapter 7 Add and Subtract Fractions
- Chapter 8 Multiply Fractions by Whole Numbers
- Chapter 9 Relate Fractions and Decimals
- Chapter 10 Two-Dimensional Figures
- Chapter 11 Angles
- Chapter 12Relative Sizes of Measurement Units
- Chapter 13 Algebra: Perimeter and Area
Grade 4 Homework Practice FL.Common Core – Grade 4 – Practice Book - Chapter 1 Place Value, Addition, and Subtraction to One Million (Pages 1- 20)
- Chapter 2 Multiply by 1-Digit Numbers (Pages 21 – 47)
- Chapter 3 Multiply 2-Digit Numbers (Pages 49- 65)
- Chapter 4 Divide by 1-Digit Numbers (Pages 67 – 93)
- Chapter 5 Factors, Multiples, and Patterns (Pages 95 – 109)
- Chapter 6 Fraction Equivalence and Comparison (Pages 111 – 129)
- Chapter 7 Add and Subtract Fractions (Pages 131 – 153)
- Chapter 8 Multiply Fractions by Whole Numbers (Pages 155- 167)
- Chapter 9 Relate Fractions and Decimals (Pages 169- 185)
- Chapter 10 Two-Dimensional Figures (Pages 187- 204)
- Chapter 11 Angles (Pages 205- 217)
- Chapter 12 Relative Sizes of Measurement Units (Pages 219- 244)
- Chapter 13 Algebra: Perimeter and Area (Pages 245- 258)
Grade 4 Homework FL. – Answer Keys- Chapter 2 Multiply by 1-Digit Numbers Review/Test
- Chapter 3 Multiply 2-Digit Numbers Review/Test
- Chapter 4 Divide by 1-Digit Numbers Review/Test
- Chapter 5 Factors, Multiples, and Patterns Review/Test
- Chapter 6 Fraction Equivalence and Comparison Review/Test
- Chapter 7 Add and Subtract Fractions Review/Test
- Chapter 8 Multiply Fractions by Whole Numbers Review/Test
- Chapter 9 Relate Fractions and Decimals Review/Test
- Chapter 10 Two-Dimensional Figures Review/Test
- Chapter 11 Angles Review/Test
- Chapter 12 Relative Sizes of Measurement Units Review/Test
- Chapter 13 Algebra: Perimeter and Area Review/Test
- Chapter 1: Place Value, Multiplication, and Expressions
- Chapter 2: Divide Whole Numbers
- Chapter 3: Add and Subtract Decimals
- Chapter 4: Multiply Decimals
- Chapter 5: Divide Decimals
- Chapter 6: Add and Subtract Fractions with Unlike Denominators
- Chapter 7: Multiply Fractions
- Chapter 8: Divide Fractions
- Chapter 9: Algebra: Patterns and Graphing
- Chapter 10: Convert Units of Measure
- Chapter 11: Geometry and Volume
- Chapter 1: Divide Multi-Digit Numbers
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Go Math Answer Key for Grade 7- Chapter 1: Adding and Subtracting Integers
- Chapter 2: Multiplying and Dividing Integers
- Chapter 3: Rational Numbers
- Chapter 4: Rates and Proportionality
- Chapter 5: Percent Increase and Decrease
- Chapter 6: Algebraic Expressions
- Chapter 7: Writing and Solving One-Step Inequalities
- Chapter 8: Modeling Geometric Figures
- Chapter 9: Circumference, Area, and Volume
- Chapter 10: Random Samples and Populations
- Chapter 11: Analyzing and Comparing Data
- Chapter 12: Experimental Probability
- Chapter 13: Theoretical Probability and Simulations
- Chapter 1 Real Numbers
- Chapter 2 Exponents and Scientific Notation
- Chapter 3 Proportional Relationships
- Chapter 4 Nonproportional Relationships
- Chapter 5 Writing Linear Equations
- Chapter 6 Functions
- Chapter 7 Solving Linear Equations
- Chapter 8 Solving Systems of Linear Equations
- Chapter 9 Transformations and Congruence
- Chapter 10 Transformations and Similarity
- Chapter 11 Angle Relationships in Parallel Lines and Triangles
- Chapter 12 The Pythagorean Theorem
- Chapter 13 Volume
- Chapter 14 Scatter Plots
- Chapter 15 Two-Way Tables
Give your kid the right amount of knowledge he needs as a part of your preparation by taking the help of our HMH Go Math Answer Key for Grades K-8. Resolve all your queries and assess your preparation standard using the Common Core Go Math Solution Key. Practicing from the Go Math Answer Key for Grades K to 8 will provide a grade by grade roadmap and prepares students for College Readiness. Gradewise HMH Go Math Answer Key provided will develop problem-solving skills among students thereby helping them to Think, Explore and Grow. The Diverse Opportunities provided helps Kids to master the content with engaging activities. Characteristics of Go Math Answer Key for Grades K to 8Go through the below-listed features of referring to the HMH Go Math Anwer Key for Grades K to 8. They are outlined as follows - All the Go Math Answer Key for Grades K to 8 are easy to download and we don’t charge any penny from you.
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FAQs on Common Core HMH Go Math Answer Key1. When Can I use the Go Math Answer Key for Grades K-8? You can use the HMH Go Math Answer Key for Grades K to 8 while practicing the Go Math Textbook Questions as a part of your Homework or Assessment and make the most out of them. 2. Is there any site that provides the Common Core Go Math Solutions Key for Grades K, 1, 2, 3, 4, 5, 6, 7, 8? Yes, you can find Go Math Answer Key for Grades K, 1, 2, 3, 4, 5, 6, 7, 8 all in one place i.e. ccssmathanswers.com a trusted and reliable portal. 3. Can I download HMH Go Math Answer Key PDF for free? Yes, you can download the HMH Math 101 Practice Key for free on our page via quick links available and we don’t charge any amount for it. Elementary School Big Ideas Math Answers- Big Ideas Math Answers Grade K
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Unit 8 - Right Triangles & Trigonometry. 9. A 35-foot wire is secured from the top of a flagpole to a stake in the ground. If the stake is 14 feet from the base of the flagpole, how tall is the flagpole? = 362 1225 32-1 10. If the diagonal of a square is I I .3 meters, approximately what is the perimeter of the square? 1 2-7.71 peri me-er- - 103.
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Chapter 8 Solutions These answers are to be used to check against your solutions. Your homework should show all of your work, not just the answers! Section 8.4 - Perpendicular Vectors 11. Inner Prod = 0; yes 13. Inner Prod = 2; no 15. Inner Prod = 32; no 17. Inner Prod = 6; no 19. Inner Prod = 9; no 21. 〈2,2,−1〉; student should show ...
This video solves the problems for the Chapter 8 HW on MyMathLab in STA 2023Here is the lesson on 8.1https://youtu.be/3P-RgYkcuBwHere is the lesson for 8.2 a...
Chapter 8 one hundred thirty-five P135 Chapter8 Dear Family, My class started Chapter 8 this week. In this chapter, I will learn how to add and subtract two-digit numbers. Love, Vocabulary ones and tens You can group ones to make tens. 20 ones = 2 tens Home Activity Using a jar and pennies, work with your child to add and subtract two-digit ...
Title: Go Math! Practice Book (TE), G5 Created Date: 12/9/2016 9:24:35 PM
Find step-by-step solutions and answers to Algebra 1 Common Core - 9780133185485, as well as thousands of textbooks so you can move forward with confidence. ... Mid-Chapter Quiz. Section 8-5: Factoring x^2 + bx + c. Section 8-6: Factoring ax^2 + bx + c. Section 8-7: Factoring Special Cases. Section 8-8: Factoring by Grouping. Page 535: Chapter ...
CPM Educational Program. With Mathleaks, you'll have instant access to expert solutions and answers to all of the CPM math questions you may have from the CPM Educational Program publications such as Pre-Algebra, Algebra 1, Algebra 2, and Geometry. Mathleaks offers the ultimate homework help and much of the content is free to use.
Course 3 • Chapter 8 Volume and Surface Area 115 ... cGraw-Hill Comp anies, Inc. Perm ission is granted to repr oduce for c lassr oom use. Lesson 1 Homework Practice Volume of Cylinders Find the volume of each cylinder. Round to the nearest tenth. 1. ... 8 in. 23 in. 3 mm 12.7 mm 2.1 cm 4.2 cm 8 ft 3 ft 6 ft h 471.2 ft3 1,156.1 in3 7.1 ft3 D ...
Everyone must do the homework for this Chapter!! You can chose to do the book homework above or the AP Classroom problems! After ch. 8 regular homework policy applies. Notes, Homework, and Reviews ... chapter 8 - Use these to help guide you while you're reading chapter 8! 1/10/20 - Practice 8.2 KEY - Quiz Monday!! 1/17/20 - Practice 8.3 KEY 1 ...
Go Math! Practice Book (TE), G5. Name Interpret Division with Fractions Write an equation to represent the problem. Then solve. Lesson 8.5 COMMON CORE STANDARD CC.5.NF.7c Apply and extend previous understandings of multiplication and division to multiply and divide fractions. 1.
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Middle School Grade 8 1st Edition, you'll learn how to solve your toughest homework problems. Our resource for Go Math! Middle School Grade 8 includes answers to chapter exercises, as well as detailed information to walk you through the process step by step. With Expert Solutions for thousands of practice problems, you can take the guesswork ...
The light-dependent reactions of photosynthesis use water and produce oxygen. True. -The water molecules are split to replenish electrons in photosystem II, leaving behind protons, which are used to generate a proton gradient for the formation of ATP, and oxygen, which is released as a by-product. Which of the following molecules is the primary ...
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Problem Solving REAL WORLD 9. There are 12 students in a jewelry-making class and 8 sets of charms. What fraction of a set of charms will each student get? Each student will get of a set. P173 Each friend will get cheesecakes. Chapter 8. Lesson Check (CC.5.NF.3) 1. Eight friends share 4 bunches of grapes equally.
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Lesson 7.8 COMMON CORE STANDARDS CC.5.NF.5a, CC.5.NF.5b Apply and extend previous understandings of multiplication and division to multiply and divide fractions. 3 equal to 3. 5. less than 15 x lg will be Think: 1 X is lg. Since is less than 1, X 15 will be less than 15. greater than 3 x 33 will be greater than 12 x 23 will be 2. -x '234 4. 9 X 14
So, students can instantly take homework help from BIM Geometry Ch 8 Similarity Answers. Simply tap on the below direct links and refer to the solutions covered in the Big Ideas Math Book Geometry Answer Key Chapter 8 Similarity Guide. Similarity Maintaining Mathematical Proficiency - Page 415; Similarity Mathematical Practices - Page 416;
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Homework Practice Workbook -07-660291-5 978--07-660291-9 Spanish Version Homework Practice Workbook -07-660294-X 978--07-660294- Answers For Workbooks The answers for Chapter 8 of these workbooks can be found in the back of this Chapter Resource Masters booklet. ... ents up to twenty of the key vocabulary terms from the chapter. Students ...
Go Math Grade K Answer Key. Chapter 1 Represent, Count, and Write Numbers 0 to 5. Chapter 2 Compare Numbers to 5. Chapter 3 Represent, Count, and Write Numbers 6 to 9. Chapter 4 Represent and Compare Numbers to 10. Chapter 5 Addition. Chapter 6 Subtraction. Chapter 7 Represent, Count, and Write 11 to 19. Chapter 8 Represent, Count, and Write 20 ...
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