homework 2 segment addition postulate answer key quizlet

Segment Addition Postulate

The segment addition postulate in geometry is applicable on a line segment containing three collinear points. It states that if there are two given points on a line segment A and C, then point B lies on the same line segment somewhere between A and C only if the sum of AB and BC is equal to AC.

By applying the segment addition postulate, we can precisely determine the length of a line segment when given specific measurements of its parts. Also, this postulate enables us to divide a line segment into different sections and explore the relation (ratios) between their lengths.

Segment Addition Postulate Definition

The segment addition postulate states that if a line segment has two endpoints, A and C, a third point B lies somewhere on the line segment AC if and only if the equation AB + BC = AC is satisfied. Look at the image given below to have a better understanding of this postulate.

If we carefully look at its name "Segment Addition Postulate", it is very easy to understand.

• A segment, here, means a line segment. It emphasis that this postulate is applicable only on a line segment, and not on a ray or a line . A line segment is part of a line bounded by two defined endpoints. We can have an infinite number of points between the endpoints of a segment.
• The "addition" means that we are adding the distances between points.
• Finally, "postulate" means this axiom is taken as a fact or valid without any proof.

Another way of stating the segment addition postulate is that if point B lies on the line segment AC, then AB + BC = AC.

Segment Addition Postulate Formula

If the end-points of a line segment are denoted as A and C, and there lies a point B on the line segment, then the segment addition postulate formula is given as AB + BC = AC.

Further, extending this theorem to two points, If there are two points B and D on the segment, we will have the formula as AB + BD + DC = AC.

☛ Related Topics:

• Segment Addition Postulate Worksheets
• Difference Between Line and Line Segment
• Line Segment

Segment Addition Postulate Examples

Example 1: In the given figure, if B is the mid-point of line segment AC, find the length of segment AC.

By using the segment addition postulate, we know that the sum of segments AB and BC is equal to AC. It can be written mathematically as AB + BC = AC. Also, B is the midpoint of AC. It implies AB = BC.

⇒ 3x = 4x-6

⇒ 6 = 4x - 3x

Now, put the value of x in the equation AB + BC = AC.

AC = 3x + 4x - 6

⇒ AC = 7x - 6

⇒ AC = 7 × 6 - 6

⇒ AC = 42 - 6

Answer: ∴ The length of the segment AC is 36 units.

Example 2: Find whether Q is the mid-point of segment PR or not, if the length of PR is 45 units. [Refer to the figure below]

Solution: There are three collinear points on the given segment which are points P, Q, and R. By using the segment addition postulate, we know that PQ + QR = PR. Substitute the value of PR as 45 units, we get,

PQ + QR = 45

⇒ 9x + 7 + (-3x+20) = 45

⇒ 9x - 3x + 7 + 20 = 45

⇒ 6x + 27 = 45

Now, let us find the values of PQ and QR.

PQ = 9x + 7 = 9 (3) + 7 = 34 units

QR = -3x+20 = -3 (3) + 20 = 11 units

Answer: ∴ PQ ≠ QR. Q is not the midpoint of segment PR.

Example 3: On a line segment XY, if Z is between X and Y and XY = 25. What will be the expression to find the value of XZ?

Solution: It is given that point Z is between X and Y, so by using the segment addition postulate, we have XZ + ZY = XY. The value of XY is given as 25. So, the expression to find the value of XZ is 25 - ZY.

Answer: ∴ 25 - ZY is the required expression.

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Practice Questions on Segment Addition Postulate

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FAQs on Segment Addition Postulate

What is segment addition postulate in geometry.

The segment addition postulate in geometry is the axiom which states that the length of a line segment divided into smaller pieces is the sum of the lengths of all those smaller segments. So, if we have three collinear points A, B, and C on segment AC such that B is somewhere between A and C, then AB + BC = AC. It is a mathematical fact that can be accepted without proof.

What are the Two Conditions of the Segment Addition Postulate?

The two conditions of the segment addition postulate are given below:

• A point P lies on a segment MN if and only if points M, P, and N are collinear taken in order.
• The distance between MP and PN must be equal to MN.

What are the Examples of Segment Addition Postulate?

As per the segment addition postulate, if we have an iron rod of length 30 inches that is cut into two parts where the length of one part is 14 inches, it means the length of the other part of the rod is 30 - 14 = 16 inches.

What is a Segment Addition Postulate Used For?

We can apply this postulate in calculating the missing lengths. It can be used to find the sum of the smaller parts of a segment to find the total length. The segment addition postulate has its applications in construction, architecture, design, etc.

How to Solve for x with Segment Addition Postulate?

If we have a missing length, let's say x, and we know the total length and the length of the other part of the segment, then we can apply the segment addition postulate to find x. For example, if AB = 3, BC = x, and AC = 5, then we can find x by subtracting AB from AC. This implies AC - AB = 5 - 3 = 2 = BC. i.e., x = 2.

How to Use the Segment Addition Postulate to Show that ae=ab+bc+cd+de?

If a segment AE has three points on it, marked as B, C, and D in order, then according to the segment addition postulate, their sum is equal. So, AE = AB + BC + CD + DE. This is possible by applying the postulate for more than one time.

What is Segment Addition Postulate in Proofs?

The segment addition postulate does not require any proof. It is accepted as a mathematical fact. But many times, we use this axiom in stating proofs for line segments. One such proof is given as "If two congruent segments are added to the line segments of the same length, then their sum is also equal."

Segment Addition Postulate

As we all know Math concepts build on each other. When it comes to Measuring Segments and the Segment Addition Postulate there are multiple lessons we must pull together to teach this lesson. The videos below do an excellent job of explaining measuring segments using the following methods.

Ruler Postulate –

Segment Addition Postulate –

Pythagorean Theorem –

Distance Formula –

Use a Manipulative to Teach the Measuring Segments

My advice would be to use blocks or cut outs like these to teach this lesson. I think establishing the connection between these real-world things and the algebra behind the geometry make these postulates much easier to learn. If you just go in with and number line and some numbers on the chalk board it probably won’t stick. I even think the measuring segments worksheets you use need to have more realistic pictures and problems in them.

Give them the squares that they can touch and manipulate. They do not have to be anything fancy. You can actually just give them square pieces of precut paper to play around with. Give them a ruler or yard stick, things they can touch and see themselves actually doing in the real world.

The Pythagorean Theorem and the Segment Addition Postulate

We also included a segment addition postulate worksheet below. These will include the problems involving distance formula, the Pythagorean Theorem , and the ruler postulate.

We also are giving you a Measuring Segments Worksheet, Exit Quiz, Bell Work Assignment, a Power Point Presentation, and some Segment Addition Postulate Guided Notes!

These Postulates Come Up Over and Over Again

Make it a lesson they won’t forget because these things come up over and over again in other lessons like…

• Absolute Value
• Constructions
• Operations with Complex Numbers
• Simplifying Radicals
• Irrational Numbers
• Pythagorean Theorem
• Square Roots

The more students hear how to develop strategies, the better they become at doing so.

Seeing these concepts used helps students make connections about the way all math concepts are related.

Here are your Free Resources for this Lesson!

Segment addition postulate worksheet, word docs & powerpoints.

To gain access to our editable content Join the Geometry Teacher Community! Here you will find hundreds of lessons, a community of teachers for support, and materials that are always up to date with the latest standards.

Segment Additions Postulate – Measuring Segments PDFs

  1-3 Assignment Student Edition- Measuring Segments  ( FREE ) 1-3 Assignment Teacher Edition – Measuring Segments ( Members Only ) 1-3 Bell Work Student Edition – Measuring Segments  ( FREE ) 1-3 Bell Work Teacher Edition – Measuring Segments ( Members Only ) 1-3 Exit Quiz Student Edition- Measuring Segments  ( FREE ) 1-3 Exit Quiz Teacher Edition – Measuring Segments ( Members Only ) 1-3 Guided Notes SE – Measuring Segments  ( FREE ) 1-3 Guided Notes Teacher Edition – Measuring Segments ( Members Only ) 1-3 Lesson Plan – Measuring Segments and the Segment Addition Postulate ( Members Only ) 1-3 Online Activities – Segment Addition Postulate ( Members Only ) 1-3 Slide Show – Measuring Segments  ( FREE )

Want access to the rest of the materials on Measuring Segments? To download the rest of the materials for this lesson and get updates via email when new lessons come out simply click the image below to Get All of Our Lessons!

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