In Segment Addition Postulate, if is between and , then + = .If = 12 and L = 5, what is the value of L?
A. 8
B. 12
C. 7
D. 5
Answers
Answer:
The segment addition postulate states that if we are given two points on a line segment, A and C, a third point B lies on the line segment AC if and only if the distances between the points meet the requirements of the equation AB + BC = AC. See Diagram 1 to gain a clearer understanding of this postulate definition.
Diagram 1: Segment Addition Postulate.
Segment Addition Postulate- Diagram 1.
Remember that a line segment is part of a line bound by two clear end points. It is comprised of a bunch of points between those two end points.
An easier way of stating the segment addition postulate is that if point B lies on line segment AC, then AB + BC will equal AC. That seems pretty simple, does it not?
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Examples
Let's take a look at some different examples.
Example 1:
Let us look at a line segment on our body: our leg! Our leg has an endpoint A, the top of your thigh, and endpoint C, your ankle. Imagine the length of your entire leg (from endpoint A to C) measures 25 inches and the length from point B, your knee, to endpoint C is 12 inches. According to the segment addition postulate, what would be the length of Endpoint A to point B?
AB (unknown) + BC (12) = AC (25)
AB = 25 - 12
AB = 13 inches
Example 2:
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Additional Activities
Additional Examples
In the following examples, students will use the Segment Addition Postulate to determine the lengths of various parts of a line segment. After completing the first few examples, students will attempt a more challenging example which uses the Segment Addition Postulate more than one time. After completing all examples, student will have confidence determining the lengths of various parts of line segments by using this postulate.
Examples
1) Point B lies on line segment AC. AB is of length 12 and BC is of length 20. How long is the entire segment AC?
2) Point Y lies on line segment XZ. XZ is of length 43 and Y is a distance of 17 from X. How far from Z is Y?
3) John works on the 19th story of a 64 story skyscraper. Use the Segment Addition Postulate to determine how many stories lie above John's floor.
4) Using the diagram below, find the length of segment BC.
Solutions
1) Since B lies on the segment AC, we know from the Segment Addition Postulate that AB + BC = AC. So we have 12 + 20 = 32.
2) Since Y is a distance of 17 from X, we know XY = 17. Since Y is on the segment XZ, we know XY + YZ = XZ. We have 17 + YZ = 43 and so YZ = 26. So Z is a distance of 26 from Y.
3) Using the Segment Addition Postulate, and letting x equal the number of stories above John's floor, we have 19 + x = 64 and so x = 45.
4) There are a few ways to find BC, and we will outline one of them. Using the information that AC = 30 and AD = 52, the Segment Addition Postulate gives us AC + CD = AD and so 30 + CD = 52, so CD = 22. Then, using the Segment Addition Postulate again, BC + CD = BD and we have BC + 22 = 37, so BC = 15.
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