body{margin:0;} noscript{z-index: 10000; position: fixed; display: block; height: 100%; width: 100%; background: #fff;} noscript .fa{font-size: 40px; display:block; color: #daa520;} noscript div{margin-top: 6%; padding-left: 20px; padding-right: 20px; text-align: center;} ! You must have JavaScript enabled to use this site.

Big Ideas Math Geometry, 2014

BI

Big Ideas Math Geometry, 2014 View details

Chapter Review

Continue to next subchapter

Exercise 13 Page 57

The midpoint divides the segment into two congruent segments.

AB= 40

Practice makes perfect

We know that M is the midpoint of AB. It is a point that divides the segment into two congruent segments.

Since AM and MB are congruent, the expressions for their lengths must be equal. We can set the two expressions equal to one another and solve for x.

3x+8=6x-4

LHS-3x=RHS-3x

8=3x-4

LHS+4=RHS+4

12=3x

.LHS /3.=.RHS /3.

4=x

Rearrange equation

x=4

The length of AB is equal to the sum of AM and MB. This is a case of the Segment Addition Postulate. AB = AM + MB We can substitute the given values and x=4 into this equation to find AB.

AB = AM + MB

AM= 3x+8, MB= 6x-4

AB = 3x+8+ 6x-4

Add terms

AB = 9x+4

x= 4

AB = 9( 4)+4

Multiply

AB = 36+4

Add terms

AB =40