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Geometry Chapter 8 Review The given polygons are similar. Find the value of x. 1. 2. 3. Find the scale factor. Then list all the pairs of congruent angles and write the ratios of the corresponding side lengths in a statement of proportionality. 4. 5. In Exercises 6 and 7, find the scale factor. Then list all pairs of congruent angles and write the ratios of the corresponding side lengths in a statement of proportionality. 6. βπΏππ to βππ π 7. ABCD to EFGH Show that the triangles are similar. Write a similarity statement. 8. 9. Can the given information be used to prove βπ¨π©πͺ~βπ¬π«πͺ? Explain your reasoning. 10. ED ο½ 8, DC ο½ 10, EC ο½ 12, AB ο½ 12, BC ο½ 15, AC ο½ 21 11. ED ο½ 7, DC ο½ 9, AB ο½ 10.5, BC ο½ 13.5, mοBAC ο« mοBCA ο½ 105ο° The triangles in each pair are similar. Find the value of x. 12. βπ·π΅πΆ~βππ π 13. βπ΄π΅πΆ~βπ·πΈπΆ 14. βπ΄π΅πΈ~βπ΄πΆπ· 15. Your geometry class goes on a field trip to the zoo. If an 18-foot tall tree casts a 9 foot-long shadow, how tall is an adult giraffe that casts a 7-foot shadow? 16. A 4-foot tall girl stands 6.5 feet from a lamp post at night. Her shadow from the light is 2.5 feet long. How tall is the lamp post? Use the figure to complete the proportion. 17. EF BA ο½ FG ? 18. CB ? ο½ BA EF 19. DC ? ο½ FA AG 20. GF GD ο½ FA ? Find the value of x. 21. 22. 23. 24. Your friend is hitting a golf ball toward the hole. The line from your friend to the hole bisects the angle formed by the lines from your friend to the oak tree and from your friend to the sand trap. The oak tree is 250 yards from him. The sand trap is 375 yards from him. The hole is 225 yards from the sand trap. How far is the hole from the oak tree? 25. Use the diagram to answer the following: a. Find the scale factor of βπ΄π΅πΆ π‘π βπππ. b. Find mοX . c. Find CD. d. Find the area of βπ΄π΅πΆ. Then find the area of βπππ. e. Find the ratio of the area of βπ΄π΅πΆ to the area of βπππ. f. Find BC and YZ . Explain your reasoning. g. Find the ratio of the perimeter of βπ΄π΅πΆ to the perimeter of βπππ. In Exercises 26 and 27, the figures are similar. Find the missing value. 26. If π΄π΅πΆπ·πΈ~πΉπΊπ»πΌπ½, AC = 6 cm, FH = 10 cm, and the area of ABCDE = 320 cm2, then the area of FGHIJ = ______________. 27. The ratio of the corresponding midsegments of two similar triangles is 4:5. What is the ratio of their areas? Answers: 1. 20 6 5 2. 10 3. 8 4. ; οC ο οD, οA ο οF , οB ο οE; AC BC AB ο½ ο½ DF DE EF 2 5 5. ; οA ο οE, οB ο οF , οC ο οG, οD ο οH ; 6. 3; ο L ο οQ, ο M ο ο R, ο N ο ο S , 2 5 AB BC AD DC ο½ ο½ ο½ EF FG EH GH LM MN NL ο½ ο½ QR RS SQ 7. ; ο A ο ο E, ο B ο ο F , οC ο οG, ο D ο ο H , AB BC CD DA ο½ ο½ ο½ EF FG GH HE 8. Sample answer: It is given that οBAC ο οEDC, and οBCA ο οECD by the Vertical Angles Congruence Theorem (Thm. 2.6). So, βπ΅π΄πΆ~βπΈπ·πΆ by the AA Similarity Theorem (Thm. 8.3); βπ΅π΄πΆ~βπΈπ·πΆ 9.Sample answer: Because BC EC ο½ and οBCA ο οECD by the Vertical Angles Congruence Theorem AC DC (Thm. 2.6), βπ΅π΄πΆ~βπΈπ·πΆ by the SAS Similarity Theorem (Thm. 8.5); βπ΅π΄πΆ~βπΈπ·πΆ 10. no; Based on this information, the triangles are not similar because the sides are not all proportional. 11. no; Although the proportion ED AB ο½ DC BC is true, there is not enough information given to determine whether οABC ο οCDE. 12. 9 13. 15 14. 6 15. 14 ft 16. 14.4 ft 17. AG 18. ED 19. CG 20. CD 21. 6 22. 11.2 23. 4.5 b. 67° c. 12 d. 60; 540 e. 9 24. 150 yd 25. a. 3 g. 3 f. 13, 39; By the SAS Congruence Theorem (Thm. 5.5), ! ADC ο ! BDC and ! XWZ ο ! YWZ . Because corresponding parts of congruent triangles are congruent, BC ο½ 13 and YZ ο½ 39. 26. 16:25 8 27. 888 9 cm2