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Splash Screen. Five-Minute Check (over Lesson 7–2) 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

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  1. Splash Screen

  2. Five-Minute Check (over Lesson 7–2) 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 Theorem 7.4: Properties of Similarity Example 4: Parts of Similar Triangles Example 5: Real-World Example: Indirect Measurement Concept Summary: Triangle Similarity Lesson Menu

  3. A B Determine whether the triangles are similar. A. Yes, corresponding angles are congruent and corresponding sides are proportional. B. No, corresponding sides are not proportional. 5-Minute Check 1

  4. A B C D 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 5-Minute Check 2

  5. A B C D 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 5-Minute Check 3

  6. A B C D 3 __ Two pentagons are similar with a scale factor of .The perimeter of the larger pentagon is 42 feet. What is the perimeter of the smaller pentagon? 7 A. 12 ft B. 14 ft C. 16 ft D. 18 ft 5-Minute Check 4

  7. You used the AAS, SSS, and SAS Congruence Theorems to prove triangles congruent. (Lesson 4–4) • Identify similar triangles using the AA Similarity Postulate and the SSS and SAS Similarity Theorems. • Use similar triangles to solve problems. Then/Now

  8. Concept

  9. Use the AA Similarity Postulate A. Determine whether the triangles are similar. If so, write a similarity statement. Explain your reasoning. Example 1

  10. Since mB = mD, B D Since mE = 80, A E. Use the AA Similarity Postulate By the Triangle Sum Theorem, 42 + 58 + mA = 180, so mA = 80. Answer:So, ΔABC ~ ΔDEC by the AA Similarity. Example 1

  11. Use the AA Similarity Postulate B. Determine whether the triangles are similar. If so, write a similarity statement. Explain your reasoning. Example 1

  12. QXP NXM by the Vertical Angles Theorem. Since QP || MN, Q N. Use the AA Similarity Postulate Answer:So, ΔQXP ~ ΔNXM by the AA Similarity. Example 1

  13. A B C D A. Determine whether the triangles are similar. If so, write a similarity statement. A. Yes; ΔABC ~ ΔFGH B. Yes; ΔABC ~ ΔGFH C. Yes; ΔABC ~ ΔHFG D. No; the triangles are not similar. Example 1

  14. A B C D B. Determine whether the triangles are similar. If so, write a similarity statement. A. Yes; ΔWVZ ~ ΔYVX B. Yes; ΔWVZ ~ ΔXVY C. Yes; ΔWVZ ~ ΔXYV D. No; the triangles are not similar. Example 1

  15. Concept

  16. Use the SSS and SAS Similarity Theorems A.Determine whether the triangles are similar. If so, write a similarity statement. Explain your reasoning. Answer:So, ΔABC ~ ΔDEC by the SSS Similarity Theorem. Example 2

  17. 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, M  M. Answer:Since the lengths of the sides that include M are proportional, ΔMNP ~ ΔMRS by the SAS Similarity Theorem. Example 2

  18. A B C D A. Determine whether the triangles are similar. If so, choose the correct similarity statement to match the given data. A.ΔPQR ~ ΔSTR by SSS Similarity Theorem B.ΔPQR ~ ΔSTR by SAS Similarity Theorem C.ΔPQR ~ ΔSTR by AAA Similarity Theorem D. The triangles are not similar. Example 2

  19. A B C D B. Determine whether the triangles are similar. If so, choose the correct similarity statement to match the given data. A.ΔAFE ~ ΔABC by SSS Similarity Theorem B.ΔAFE ~ ΔACB by SSS Similarity Theorem C.ΔAFE ~ ΔAFC by SSS Similarity Theorem D.ΔAFE ~ ΔBCA by SSS Similarity Theorem Example 2

  20. If ΔRST and ΔXYZ are two triangles such that = which of the following would be sufficient to prove that the triangles are similar?A BC R  S D 2 __ RS ___ 3 XY Example 3

  21. Read the Test Item You are given that = and asked to identify which additional information would be sufficient to prove that ΔRST ~ ΔXYZ. 2 __ RS ___ 3 XY Example 3

  22. Solve the Test Item Since = , you know that these two sides are proportional at the scale factor of . Check each answer choice until you find one that supplies sufficient information to prove that ΔRST ~ ΔXYZ. 2 2 __ __ RS ___ 3 3 XY Example 3

  23. Choice A If = , then you know that the other two sides are proportional. You do not, however, know whether that scale factor is as determined by . Therefore, this is not sufficient information. 2 __ RT ST RS ___ ___ ___ 3 XZ YZ XY Example 3

  24. Choice B If = = , then you know that all the sides are proportional by the same scale factor, . This is sufficient information by the SSS Similarity Theorem to determine that the triangles are similar. 2 __ RS RT RT ___ ___ ___ 3 XY XZ XZ Answer: B Example 3

  25. A B C D A. = B.mA = 2mD C.= D. = 4 4 __ __ AC BC BC AC ___ ___ ___ ___ 3 5 DC DC DC EC Given ΔABC and ΔDEC, which of the following would be sufficient information to prove the triangles are similar? Example 3

  26. ALGEBRAGiven , RS = 4, RQ = x + 3, QT= 2x + 10, UT = 10, find RQ and QT. Parts of Similar Triangles Example 4

  27. Since because they are alternate interior angles. By AA Similarity, ΔRSQ ~ ΔTUQ. Using the definition of similar polygons, Parts of Similar Triangles Substitution Cross Products Property Example 4

  28. Parts of Similar Triangles Distributive Property Subtract 8x and 30 from each side. Divide each side by 2. Now find RQ and QT. Answer:RQ = 8; QT = 20 Example 4

  29. A B C D ALGEBRAGiven AB = 38.5, DE = 11, AC = 3x + 8, and CE =x + 2, find AC. A. 2 B. 4 C. 12 D. 14 Example 4

  30. Concept

  31. P 479 9, 11, 14, 16 – 20 even

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