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McGraw Hill Integrated II, 2012 View details

4. Parallel Lines and Proportional Parts

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Exercise 34 Page 579

Write a proportion using the Corresponding Angles Theorem and the Angle-Angle Similarity Theorem.

8

Practice makes perfect

Let's analyze the given figure.

Since PT is parallel to QR, according to the Corresponding Angles Theorem ∠ SPT is congruent to ∠ SQR, and ∠ STP is congruent to ∠ SRQ. Therefore, by the Angle-Angle Similarity Theorem △ QRS is similar to △ PTS. Let's write a proportion using the expressions for the lengths of the sides of both triangles. SP/SQ=PT/QR ⇕ 4/SQ=6/12 Finally, we will solve this equation for SQ.

4/SQ=6/12

▼

Solve for SQ

MultEqn

LHS * SQ=RHS* SQ

4=6/12SQ

ReduceFrac

a/b=.a /6./.b /6.

4=1/2SQ

MultEqn

LHS * 2=RHS* 2

8=SQ