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McGraw Hill Integrated II, 2012 View details

4. Parallel Lines and Proportional Parts

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Exercise 36 Page 579

Write a proportion using the Triangle Proportionality Theorem.

WY=21

Practice makes perfect

Let's analyze the given figure. Since we are given a triangle with a line that is parallel to one of its sides, we can use the Triangle Proportionality Theorem.

The lengths of the segments intercepted by the parallel line are proportional. Let's write a proportion using the expressions for the lengths of the segments. WV/VZ=WX/XY ⇕ 6/a-9=7/XY Since we are given the lengths of WX and WY, we can find the length of XY.

WX+XY=WY

SubstituteII

WX= 7, WY= a

7+XY= a

SubEqn

LHS-7=RHS-7

XY=a-7

Now we can substitute the missing length into our proportion. 6/a-9=7/XY ⇕ 6/a-9=7/a-7 Finally, we will solve this equation for a.

6/a-9=7/a-7

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Solve for a

MultEqn