Warm-Up Exercises

ANSWER 8

1. Give the postulate or theorem that justifies why the triangles are similar.

2. Solve = .1632

12 – x x

ANSWER AA Similarity Postulate

Warm-Up ExercisesEXAMPLE 1 Find the length of a segment

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=

RQ 9

46=

Warm-Up ExercisesEXAMPLE 2 Solve a real-world problem

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.

Shoerack

SOLUTION

Find and simplify the ratios of lengths determined by the shoerack.

CBBA

2733= 9

11=CD

DE4425=

Warm-Up ExercisesEXAMPLE 2 Solve a real-world problem

Because , BD is not parallel to AE .

So, the shelf is not parallel to the floor.

4425

911=

ANSWER

Warm-Up ExercisesGUIDED PRACTICE for Examples 1 and 2

1. Find the length of YZ .

31511ANSWER

2. Determine whether PS || QR .

ANSWER parallel

Warm-Up ExercisesEXAMPLE 3 Use Theorem 6.6

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.

Warm-Up Exercises

HG + GF GF

CD + DE DE=

EXAMPLE 3

HGGF

CDDE= Parallel lines divide transversals

proportionally.

Property of proportions (Property 4)

Substitute.

HF = 360

HF120

300+150 150=

450150

HF120 = Simplify.

Multiply each side by 120 and simplify.

The distance between Main Street and South Main Street is 360 yards.

Use Theorem 6.6

Warm-Up Exercises

SOLUTION

EXAMPLE 4 Use Theorem 6.7

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.

Warm-Up ExercisesEXAMPLE 4 Use Theorem 6.7

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.

Warm-Up ExercisesGUIDED PRACTICE for Examples 3 and 4

Find the length of AB.

3.

ANSWER 19.2

4. ANSWER 24

Warm-Up ExercisesDaily Homework Quiz

Find the value of the variable.

1.

ANSWER 12

Warm-Up ExercisesDaily Homework Quiz

Find the value of the variable.

2.

ANSWER 13.5

Warm-Up ExercisesDaily Homework Quiz

Find the value of the variable.

3.

ANSWER 23.8

Warm-Up ExercisesDaily Homework Quiz

4. This diagram represents a tract of land being developed for homes. Which lot has the greatest perimeter?

ANSWER Lot C