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Segment Addition Postulate

By Vighnesh Hemnani

Segment Addition Postulate is a mouthful, but it is a simple concept that is explained simply at Thinkster. Check out our solved example and practice problems for you to work on!

Why is this concept useful?

A common question asked when learning this topic is: “if this whole postulate is intuitive, then why do we need it?”. In Mathematics, simply knowing that 1 + 1 = 2 may not be enough – it is important to declare postulates and theorems because it is the foundation upon which we base other theories. We build on knowledge based on concepts that we firmly believe in and know and can relate to outside the textbook. Segment Addition Postulate is a concept that is very applicable in the real world too – it’s how you measure distances from one place to another!

Where does this concept fit into the curriculum?

High School Geometry

What is the Segment Addition Postulate?

By definition, the Segment Addition Postulate is a statement that says if we know that there are two points, A and C, along a line segment, then a point B must lie on the same line segment AC if the distances in the following equation add up:

AB + BC = AC

Here’s a simple diagram that depicts this rule:

In short, a point B, can only lie in the middle of two points on a line, if the distances in between B, add up to the whole distance – this is pretty intuitive!

How to use this concept?

Segment addition postulate can be used in many ways and you can be asked to solve for a number of missing quantities. The main idea is that often times, a question will ask you to solve for a missing quantity, usually one missing from the following equation:

AB + BC = AC

You can use the above formula from the Segment Addition Postulate to be able to arrive at an answer that will tell you everything about a line segment.

Sample Math Problems

Question

Find the missing length NO given that the total length MO is 9 and MN is 7

Answer

By the Segment Addition Postulate, we know that:

MN + NO = MO

7 + NO = 9

NO = 9 – 7

NO = 2

Question

If we know that the length AC is 32 and the length BC is 17, then what is the length of AB?

Answer

Based on the Segment Addition Postulate, we can say that:

AB + BC = AC

AB + 17 = 32

AB = 32 – 17

AB = 15

Question

In the below diagram, there are some distances provided. In addition, if you know that the total length from A to C is x + 12, then what is the value of x?

Answer

Again, the algebraic unknown is just a way to throw people off – if we stick to the Segment Addition Postulate, we should get the following:

AB + BC = AC

6 + 3x + 6 = x + 12

3x + 12 = x + 12

3x = x

2x = 0

x = 0

Tip: Just because you got x = 0 doesn’t mean it’s wrong or that there is an error with the question. Remember that the value of x doesn’t directly mean any distance. If you want to calculate the distances, you need to plug x back into either 3x + 6 to get 6, or x + 12 to get 12.

Question

Given the total length from WZ is 20 and the following information, find the value of x:

Answer

This time, unlike the previous examples or the definition of Segment Addition Postulate, includes a line with more than 3 points. However, the beauty of this postulate is that it can be extrapolated to more than 3 points. The same concept is just applied again (the sum of each line segment adds up to the length of the whole line segment):

WX + XY + YZ = WZ

2x – 12 + 10 + x – 10 = 20

x – 12 = 20

x = 20 + 12

x = 32

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Practice Math Problems

1. If you were to know that the length of DG is 5x – 24, then find x based on the following diagram and information provided:

2. Let us say that there is a line upon which there are the collinear points J, K, L, M and N (in that specific order). Supposing that the length of JN is x + 39 and the length of LN is x + 29.

3. Given that the points T, U, V are collinear, those points are in that order on a line segment and the following information, what is the length of TV?

TV = 2x + 1 , TU = x – 2, UV = 14

4. Find the length of QS given the following conditions:

  • points Q, R and S are collinear
  • R is between point Q and S
  • QR = 14
  • RS = 3

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