Over Lesson 7 2 Determine whether the triangles are similar. The quadrilaterals are similar. Find the scale factor of the larger quadrilateral to the
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1 Five-Minute Check (over Lesson 7 2) CCSS Then/Now Postulate 7.1: Angle-Angle (AA) Similarity Example 1: Use the AA Similarity Postulate Theorems Proof: Theorem 7.2 Example 2: Use the SSS and SAS Similarity Theorems Example 3: Standardized Test Example: Sufficient Conditions Theorem 7.4: Properties of Similarity Example 4: Parts of Similar Triangles Example 5: Real-World Example: Indirect Measurement Concept Summary: Triangle Similarity 1
2 Over Lesson 7 2 Determine whether the triangles are similar. The quadrilaterals are similar. Find the scale factor of the larger quadrilateral to the smaller quadrilateral. The triangles are similar. Find x and y. 3 Two pentagons are similar with a scale factor of 7 The perimeter of the larger pentagon is 42 feet. What is the perimeter of the smaller pentagon? Over Lesson 7 2 Determine whether the triangles are similar. A. Yes, corresponding angles are congruent and corresponding sides are proportional. B. No, corresponding sides are not proportional. 2
3 Over Lesson 7 2 The quadrilaterals are similar. Find the scale factor of the larger quadrilateral to the smaller quadrilateral. A. 5:3 B. 4:3 C. 3:2 D. 2:1 Over Lesson 7 2 The triangles are similar. Find x and y. A. x = 5.5, y = 12.9 B. x = 8.5, y = 9.5 C. x = 5, y = 7.5 D. x = 9.5, y = 8.5 3
4 A. 12 ft Over Lesson Two pentagons are similar with a scale factor of 7. The perimeter of the larger pentagon is 42 feet. What is the perimeter of the smaller pentagon? B. 14 ft C. 16 ft D. 18 ft Content Standards G.SRT.4 Prove theorems about triangles. G.SRT.5 Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures. Mathematical Practices 4 Model with mathematics. 7 Look for and make use of structure. 4
5 You used the AAS, SSS, and SAS Congruence Theorems to prove triangles congruent. Identify similar triangles using the AA Similarity Postulate and the SSS and SAS Similarity Theorems. Use similar triangles to solve problems. 5
6 Use the AA Similarity Postulate A. Determine whether the triangles are similar. If so, write a similarity statement. Explain your reasoning. Recall: + + = =180 =80 Notice: = =80 and = =42 Thus: and Answer: So, ABC ~ EDF by the AA Similarity. 80 Use the AA Similarity Postulate B. Determine whether the triangles are similar. If so, write a similarity statement. Explain your reasoning. By AIAT: and Answer: So, QXP ~ NXM by AA Similarity. 6
7 A. Determine whether the triangles are similar. If so, write a similarity statement. A. Yes; ABC ~ FGH B. Yes; ABC ~ GFH C. Yes; ABC ~ HFG D. No; the triangles are not similar. B. Determine whether the triangles are similar. If so, write a similarity statement. A. Yes; WVZ ~ YVX B. Yes; WVZ ~ XVY C. Yes; WVZ ~ XYV D. No; the triangles are not similar. 7
8 Use the SSS and SAS Similarity Theorems A. Determine whether the triangles are similar. If so, write a similarity statement. Explain your reasoning. Compare:,, =9 6 =3 2 =6 4 =3 2 =7.5 5 =3 2 Answer: So, ABC ~ DEC by the SSS Similarity Theorem. 8
9 Use the SSS and SAS Similarity Theorems B. Determine whether the triangles are similar. If so, write a similarity statement. Explain your reasoning. By the Reflexive Property, = =10 25 =2 5 = =12 30 =2 5 Answer: Since the lengths of the sides that include M are proportional, MNP ~ MRS by the SAS Similarity Theorem. A. Determine whether the triangles are similar. If so, choose the correct similarity statement to match the given data. A. PQR ~ STR by SSS Similarity Theorem B. PQR ~ STR by SAS Similarity Theorem C. PQR ~ STR by AA Similarity Theorem D. The triangles are not similar. 9
10 B. Determine whether the triangles are similar. If so, choose the correct similarity statement to match the given data. A. AFE ~ ABC by SAS Similarity Theorem B. AFE ~ ABC by SSS Similarity Theorem C. AFE ~ ACB by SAS Similarity Theorem D. AFE ~ ACB by SSS Similarity Theorem If RST and XYZ are two triangles such that RS = 2, which of the following would be sufficient XY 3 to prove that the triangles are similar? A B Sufficient Conditions C R S D 10
11 Given ABC and DEC, which of the following would be sufficient information to prove the triangles are similar? A. AC = DC B. m A = 2m D C. AC = DC D. BC = DC 4 3 BC EC
12 Parts of Similar Triangles ALGEBRA Given, RS = 4, RQ = x + 3, QT = 2x + 10, UT = 10, find RQ and QT. UTQ~ SRQ by AA since by AIAT So = = = 5 +3 =2(2 +10) 5 +15=4 +20) =5 = +3=5+3=8 =2 +10= =20 Answer: RQ = 8; QT = 20 ALGEBRA Given AB = 38.5, DE = 11, AC = 3x + 8, and CE = x + 2, find AC. A. 2 B. 4 C. 12 D
13 Indirect Measurement SKYSCRAPERS Josh wanted to measure the height of the Sears Tower in Chicago. He used a 12-foot light pole and measured its shadow at 1 p.m. The length of the shadow was 2 feet. Then he measured the length of Sears Tower s shadow and it was 242 feet at the same time. What is the height of the Sears Tower? Understand Make a sketch of the situation. Indirect Measurement SKYSCRAPERS Josh wanted to measure the height of the Sears Tower in Chicago. He used a 12-foot light pole and measured its shadow at 1 p.m. The length of the shadow was 2 feet. Then he measured the length of Sears Tower s shadow and it was 242 feet at the same time. What is the height of the Sears Tower? 242 =12 2 = 12(242) 2 =1452 Answer: The Sears Tower is 1452 feet tall. 13
14 LIGHTHOUSES On her trip along the East coast, Jennie stops to look at the tallest lighthouse in the U.S. located at Cape Hatteras, North Carolina. At that particular time of day, Jennie measures her shadow to be 1 foot 6 inches in length and the length of the shadow of the lighthouse to be 53 feet 6 inches. Jennie knows that her height is 5 feet 6 inches. What is the height of the Cape Hatteras lighthouse to the nearest foot? A. 196 ft B. 39 ft C. 441 ft D. 89 ft 14
15 15
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