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McGraw Hill Integrated II, 2012

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McGraw Hill Integrated II, 2012 View details

6. Trapezoids and Kites

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Exercise 44 Page 528

Use the Trapezoid Midsegment Theorem.

8

Practice makes perfect

We want to find the length of TS.

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. 13=1/2 (( 2x+2)+( 5x+3)) By performing inverse operations, we can solve this equation for x.

13=1/2 ((2x+2)+(5x+3))

▼

Solve for x

Remove parentheses

13=1/2(2x+2+5x+3)

Add terms

13=1/2(7x+5)

LHS * 2=RHS* 2

26=7x+5

LHS-5=RHS-5

21=7x

.LHS /7.=.RHS /7.

3=x

Rearrange equation

x=3

We found the value of x=3. TS=2x+2 ⇕ TS=2(3)+2=8

Subchapter links

Exercises p.526-530