body{margin:0;} noscript{z-index: 10000; position: fixed; display: block; height: 100%; width: 100%; background: #fff;} noscript .fa{font-size: 40px; display:block; color: #daa520;} noscript div{margin-top: 6%; padding-left: 20px; padding-right: 20px; text-align: center;} ! You must have JavaScript enabled to use this site.

McGraw Hill Integrated II, 2012

MH

McGraw Hill Integrated II, 2012 View details

4. Parallel Lines and Proportional Parts

Continue to next subchapter

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