6.66.6 Use Proportionality Theorems

Bell Thinger

ANSWER 8

1. Give the postulate or

theorem that justifies why

the triangles are similar.

2. Solve = .3216 12 – x

x

ANSWER AA Similarity Postulate

6.6

6.6Example 1

In the diagram, QS || UT , RS = 4,

ST = 6, and QU = 9. What is the

length of RQ ?

SOLUTION

Triangle Proportionality Theorem

Substitute.

Multiply each side by 9 and simplify.RQ = 6

RQQU

RSST

=

RQ9

46=

6.6Example 2

Shoerack

SOLUTION

Find and simplify the ratios of lengths determined by

the shoerack.

CBBA

2733

=9

11=CD

DE4425

=

On the shoerack

shown, AB = 33 cm, BC = 27

cm, CD = 44 cm,and DE = 25 cm.

Explain why the gray shelf is

not parallel to the floor.

Because , BD is not parallel to AE .

So, the shelf is not parallel to the floor.

4425

911

=

6.6Guided Practice

1. Find the length of YZ .

31511ANSWER

2. Determine whether PS || QR .

ANSWER parallel

6.6

6.6Example 3

In the

diagram, 1, 2, and 3 are all

congruent and GF = 120 yards, DE

= 150 yards, and CD = 300 yards.

Find the distance HF between

Main Street and South Main

Street.

City Travel

SOLUTION

Corresponding angles are congruent, so

FE, GD , and HC are parallel. Use Theorem 6.6.

6.6

HG + GFGF

CD + DEDE

=

HGGF

CDDE

= Parallel lines divide transversals

proportionally.

Property of proportions

(Property 4)

Substitute.

HF = 360

HF120

300+150150=

450150

HF120

= Simplify.

Multiply each side by 120 and

simplify.

The distance between Main Street and South Main

Street is 360 yards.

Example 3

6.6Example 4

SOLUTION

In the diagram, QPR RPS. Use

the given side lengths to find the

length of RS .

Because PR is an angle bisector of

QPS, you can apply Theorem 6.7. Let RS = x.

Then RQ = 15 – x.

7x = 195 – 13x Cross Products Property

x = 9.75 Solve for x.

RQRS

PQPS

=

15 – x

x=

73

Angle bisector divides opposite

side proportionally.

Substitute.

6.6Guided Practice

Find the length of AB.

3. ANSWER 19.2

4. ANSWER 4 2

6.6Exit Slip

Find the value of the variable.

1.ANSWER 12

6.6

Find the value of the variable.

2.

ANSWER 13.5

Exit Slip

6.6

Find the value of the variable.

ANSWER 23.8

3.

Exit Slip

6.6

4. This diagram represents a tract of land being

developed for homes. Which lot has the greatest

perimeter?

ANSWER Lot B

Exit Slip

6.6

No ANSWERANSWER Yes; XYZ ~ CBA

Exit Slip

6.6

Homework

Pg 418-421

#5, 10, 16, 21, 24