1. 1. Give the postulate or theorem that justifies why the triangles are similar.
ANSWER
AA Similarity Postulate
2. Solve = 16 32
12 – x x
ANSWER 8

2. Find the length of a segment
EXAMPLE 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 RQ QU RS ST =
Triangle Proportionality Theorem RQ 9 4 6 =
Substitute.
RQ = 6
Multiply each side by 9 and simplify.

3. EXAMPLE 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. CD DE 44 25 = CB BA 27 33 = 9 11

4. EXAMPLE 2
Solve a real-world problem
Because , BD is not parallel to AE .
So, the shelf is not parallel to the floor. 44 25 9 11 =
ANSWER

5. GUIDED PRACTICE
for Examples 1 and 2
1. Find the length of YZ .
315 11
ANSWER
2. Determine whether PS || QR .
ANSWER
parallel

6. EXAMPLE 3
Use Theorem 6.6
In the diagram, 1, 2, and are all congruent and GF = 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.

7. The distance between Main Street and South Main Street is 360 yards.
EXAMPLE 3
Use Theorem 6.6 HG GF CD DE =
Parallel lines divide transversals proportionally.
HG + GF GF
CD + DE DE =
Property of proportions (Property 4) HF
120
150 =
Substitute.
450
150 HF
120 =
Simplify.
HF =
Multiply each side by 120 and simplify.
The distance between Main Street and South Main Street is 360 yards.

8. EXAMPLE 4
Use Theorem 6.7
In the diagram, QPR RPS. Use the given side lengths to find the length of RS . ~
SOLUTION
Because PR is an angle bisector of QPS, you can apply Theorem 6.7. Let RS = x. Then RQ = 15 – x.

9. EXAMPLE 4 Use Theorem 6.7 RQ RS PQ PS = 15 – x x = 7 3 7x = 195 – 13x
Angle bisector divides opposite side proportionally.
15 – x x = 7 3
Substitute.
7x = 195 – 13x
Cross Products Property
x = 9.75
Solve for x.

10. GUIDED PRACTICE
for Examples 3 and 4
Find the length of AB. 3.
ANSWER
19.2 4.
ANSWER 2 4

11. Daily Homework Quiz
Find the value of the variable. 1.
ANSWER 12

12. Daily Homework Quiz
Find the value of the variable. 2.
ANSWER
13.5

13. Daily Homework Quiz
Find the value of the variable. 3.
ANSWER
23.8

14. Daily Homework Quiz
4. This diagram represents a tract of land being developed for homes. Which lot has the greatest perimeter?
ANSWER
Lot C