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Big Ideas Math Integrated I, 2016 View details

Chapter Review

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Exercise 13 Page 433

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

SubEqn

LHS-3x=RHS-3x

8=3x-4

AddEqn

LHS+4=RHS+4

12=3x

DivEqn

.LHS /3.=.RHS /3.

4=x

RearrangeEqn

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

SubstituteII

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

AB = 3x+8+ 6x-4

AddTerms

Add terms

AB = 9x+4

Substitute

x= 4

AB = 9( 4)+4

Multiply

AB = 36+4