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.

Dashboard

McGraw Hill Integrated II, 2012 View details

Study Guide and Review

Continue to next subchapter

Exercise 28 Page 609

Write a proportion using the Triangle Angle Bisector Theorem.

≈ 18.9

Practice makes perfect

Let's analyze the given figure.

Since we are given a triangle with a segment that bisects one of the angles, we can use the Triangle Angle Bisector Theorem.

This theorem tells us that an angle bisector in a triangle separates the opposite side into two segments that are proportional to the lengths of the other two sides. We are given the expressions for the lengths of these sides and segments, so we can write a proportion. 36-w/w = 9/10 Let's solve it using the Cross Product Property.

36-w/w = 9/10

▼

Solve for w

CrossMult

Cross multiply

(36-w)10=9w

Distr

Distribute 10

360-10w=9w

AddEqn

LHS+10w=RHS+10w

360=19w