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Answers for the lesson “Prove Triangles Similar by SSS and SAS” LESSON 6.4 11. nABC , nDEC; ACB > Skill Practice DCE by the Vertical Angles Congruence Theorem and 1. PX, CB, PQ 2. You would need to know that 15 12 3 18 3. } 5 } 5 }; } 10 8 2 12 16 20 2 10 4. } 5 } 5 }; } 40 50 5 25 5. nRST BC EC AC DC 3 2 } 5 } 5 }. The triangles are one pair of corresponding sides is congruent. similar using the SAS Similarity Theorem. 12. nXYZ , nDJG; D > X and DJ XY DG XZ 5 3 } 5 } 5 }. The triangles are 6. nJKL similar by the SAS Similarity Theorem. 7. similar; nFDE , nXWY; 2 : 3 8. not similar 13. Sample answer: The triangle 9. 3; correspondence is not listed in the correct order; nABC , nRQP. Copyright © Houghton Mifflin Harcourt Publishing Company. All rights reserved. X 4(n 1) P 5 Z 15. 4 R 14. D Z 7n 1 Y X 10. Sample answer: 34 Y N FH HK nGHJ , nFHK; } 5} HJ GH KF 66 80 4 5} 5 }3 thus the triangles JG are similar by the SSS Similarity Theorem. L 34 M They are similar by the AA Similarity Postulate. Geometry Answer Transparencies for Checking Homework 178 T 16. 27. In similar triangles the ratio of 32 16 20 S the areas is the square of the scale factor. Sample answer: Let the base and height of nVWX measure 3a and 3b and the base and height of nABC measure 2a and 2b. The ratio of their areas is F R 48 24 H 30 G 3a(3b) 2 } 2a(2b) } 2 } They are not similar since the larger side in nRST would not be opposite the largest angle. 9 5 }4. Problem Solving 17. E 15 D 28. AA Similarity Postulate; in 7x nAGB A and AGB are congruent to A and AFC in nAFC. InnAFC A and AFC are congruent to A and AED in nAED. F 25 B Copyright © Houghton Mifflin Harcourt Publishing Company. All rights reserved. 24 A 8x C 54 29. The triangle whose sides measure They are not similar since the ratio of corresponding sides is not constant for any arrangement of side lengths. 18. 538 19. 458 20. 828 21. 24 22. 42 23. 16Ï 2 24. nNSM and nNRP, nNSL and nNRQ, nNLM and nNQP 3 25. } 2 } 4 inches, 4 inches, and 7 inches is similar to the triangle whose sides measure 3 inches, 3 inches, and 5.25 inches. CD 30. } is the same scale factor as CE the other ratio. 31. CBD > CAE 9 26. } 4 Geometry Answer Transparencies for Checking Homework 179 36. Yes. Sample answer: All pairs 32. of similar triangles have angle pairs whose measures are in proportion (with constant of proportionality 1). 10 20 8 5 20 4 nXYW is not similar to nXZW. 33. a. AA Similarity Postulate b. 80 ft c. 70.8 ft AB GB 6 Copyright © Houghton Mifflin Harcourt Publishing Company. All rights reserved. so that GB 5 DE. Draw } GH so } } that GH i AC. This makes n ABC , nGBH by the AA Similarity Postulate. From this similarity you have AC GH } 5 }. Using this along with 34. a. 8, 24; 18 37. Sample answer: Locate G on } AB 30 10 8 24 1 b. } 3 c. yes; yes GH GB 5} what’s given, you get } DE DF GH > } DF, which implies that } making nGBH > nDEF. Finally, use the definition of congruent triangles and the AA Similarity Postulate to conclude n ABC , nDEF. 38. about 15.4 ft 35. Sample answer: Given that D and } and BC } E are midpoints of AB respectively the Midsegment Theorem guarantees that } }. By the Corresponding AC i DE Angles Postulate A > BDE and so BDE is a right angle. } i EF }. By Reasoning similarly AB the Alternate Interior Angles Congruence Theorem BDE > DEF. This makes DEF a right angle that measures 908. Geometry Answer Transparencies for Checking Homework 180 Mixed Review of Problem Solving 3. Dilation with scale factor 3 and then a translation right. 1. Sample: 4. Yes; triangle SRQ is a dilation and reflection of triangle LMN. U 3 cm V 4 cm W E 2.5 cm 2 cm 7. a. Use the AA Similarity F 1 Scale factor: }2 2. 7.2; 7 Copyright © Houghton Mifflin Harcourt Publishing Company. All rights reserved. LMN, side MN would match with RS, but side LM would not line up with side QS. XY XW 6. } 5 } XZ XV D 1.5 cm 5. No; After a dilation of triangle 5 cm . 2 Postulate since D and B are right angles and ACB > ECD by the Vertical Angles Congruence Theorem. b. 1.5 mi c. 12.5 mi Geometry Answer Transparencies for Checking Homework 181