1. Give the postulate or theorem that justifies why the triangles are similar. ANSWER AA Similarity Postulate 2. Solve = .

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Presentation transcript:

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

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.

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

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

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

EXAMPLE 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.

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 120 300+150 150 = Substitute. 450 150 HF 120 = Simplify. HF = 360 Multiply each side by 120 and simplify. The distance between Main Street and South Main Street is 360 yards.

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.

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.

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

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

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

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

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