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
