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McGraw Hill Integrated II, 2012

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McGraw Hill Integrated II, 2012 View details

4. Parallel Lines and Proportional Parts

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Exercise 33 Page 579

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

9

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. ST/SR=PT/QR Since we are given lengths of ST and TR, we can find length of SR.

ST+TR=SR

ST= 8, TR= 4

8+ 4=SR

▼

Solve for SR

Add terms

12=SR

Rearrange equation

SR=12

Now we can substitute all known lengths into our proportion. ST/SR=PT/QR ⇕ 8/12=6/QR Finally, we will solve this equation for QR.

8/12=6/QR

▼

Solve for QR

LHS * QR=RHS* QR

8/12QR=6

a/b=.a /4./.b /4.

2/3QR=6

LHS * 3=RHS* 3

2QR=18

.LHS /2.=.RHS /2.

QR=9

Subchapter links

Exercises p.577-581