Segment addition postulate

The segment addition postulate states the following for 3 points that are collinear.  


Consider the segment on the right.  

collinear points


If 3 points A, B, and C are collinear and B is between A and C, then

AB + BC = AC


Using the segment addition postulate


Suppose AC =  48, find the value of x. Then, find AB and BC

AB + BC = AC

( 2x - 4 ) +( 3x + 2 ) = 48

2x + 3x - 4 + 2 = 48

5x - 4 + 2 = 48

Add 4 to both sides of the equation

5x - 4 + 4 + 2 = 48 + 4

5x + 2 = 52

Subtract 2 from both sides

5x + 2 - 2 = 52 - 2

5x = 50

Divide both sides by 5

5x / 5 = 50 / 5

x = 10

AB = 2x - 4

AB = 2 × 10 - 4

AB = 20 - 4 = 16

BC = 3x + 2

BC = 3 × 10 + 2

BC = 30 + 2 = 32


Segment addition postulate and the midpoint

Suppose XA = 3x and AY =  4x - 6. If A is the midpoint of XY, what is the length of XY?

                        3x                       4x - 6
              _________________________________
              X                         A                         Y

If A is the midpoint, XA = AY.

3x = 4x - 6

Subtract 3x from both sides

3x - 3x = 4x - 3x - 6

0  = x - 6

Add 6 to both sides of the equation

0 + 6 = x - 6 + 6

6 = x

XA = AY = 3 × 6 = 16

XY = XA + AY = 16 + 16 = 32







Recent Articles

  1. Bessy and Bob algebra word problem

    Jul 28, 17 02:38 PM

    Bessy has 6 times as much money as Bob, but when each earn $6. Bessy will have 3 times as much money as Bob. How much does each have before and after

    Read More

New math lessons

Your email is safe with us. We will only use it to inform you about new math lessons.

            Follow me on Pinterest


Page copy protected against web site content infringement by Copyscape