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McGraw Hill Integrated II, 2012 View details

6. Trapezoids and Kites

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Exercise 43 Page 528

Use the Trapezoid Midsegment Theorem.

20

Practice makes perfect

We want to find the length of PM.

Recall the Trapezoid Midsegment Theorem.

Trapezoid Midsegment Theorem
The midsegment of a trapezoid is parallel to each base and its measure is one half the sum of the lengths of the bases.

Using the theorem, we can write the following equation. PM= 1/2 ( TS+ QR) Let's substitute the given lengths of the segments into the equation. 2x=1/2 ( 10+ 3x) By performing inverse operations, we can solve this equation for x.

2x=1/2(10+3x)

▼

Solve for x

MultEqn

LHS * 2=RHS* 2

4x=10+3x

SubEqn

LHS-3x=RHS-3x

x=10

We found the value of x=10. PM=2x ⇕ PM=2(10)=20