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NAME_____________________________________DATE________________PER.________ 7.2 β SIMILAR POLYGONS Use the figures below to answer the questions that follow. 1. __________ β π΄ β ? M B 2. __________ Μ Μ Μ Μ π΄π΅ βΆ ? 3. __________ Μ Μ Μ Μ βΆ ? πΆπ΄ 4. __________ β π β ? 5. __________ β πΆ β ? 6. __________ Μ Μ Μ Μ Μ βΆ ? ππ A οΎ C 7. __________ Name the side included between β π΄ and β π΅. 8. __________ Μ Μ Μ Μ Μ and πΏπ Μ Μ Μ Μ . Name the angle included between ππ 9. __________ Μ Μ Μ Μ . Name the angle included between Μ Μ Μ Μ π΄πΆ and π΅πΆ 10. __________ Name the side included between β πΏ and β π. If πΈπππ π³π΄π΅πΆ is similar to πΈπππ πΎπΏππ, name the following. 11. __________ β πΏ β ? 12. __________ Μ Μ Μ Μ Μ βΆ ? ππ 13. __________ β π β ? 14. __________ Μ Μ Μ Μ Μ βΆ ? ππ 15. __________ Μ Μ Μ Μ Μ and ππ Μ Μ Μ Μ ? What angle is included between ππ 16. __________ What side is included between β π and β π? L N 17. a) β π΄ β __________ π΄π΅πΆπ·~ππππ below. Use these figures to answer the questions. b) β π΅ β _________ A B c) β πΆ β __________ W X d) β π· β _________ e) π΄π΅ = 18. YES ππ or = NO Z C D π΅πΆ Y Are the two triangles shown below similar? F C Explain: 8 ππ A 12 ππ 110° 38° 6 ππ 12 ππ 18 ππ 32° B D 110° E 9 ππ 19. __________ What is the scale factor of βπΉπ·πΈ to βπΆπ΄π΅ in problem #2? 20. __________ What is the ratio of the perimeter of βπΉπ·πΈ to βπΆπ΄π΅? 21. __________ How do the scale factor and ratio of the perimeters of βπΉπ·πΈ to βπΆπ΄π΅ compare? For each of the following, each pair of polygons is similar. Find the values of βπβ and βπβ. F 22. π₯ = _________ π¦ =__________ A 15 π₯ + 2 D B 8 π¦β3 5 10 C H I H 23. π₯ = __________ G E M ππ° π¦ = __________ G ππ° N (π + ππ)° J L (π β ππ)° ππ° O K 24. π₯ = __________ π π¦ = __________ π° R ππ π π ππ° ππ° J L Q 25. π₯ = __________ T D ππ ππ π¦ = __________ G ππ ππ ππ ππ ππ + π E ππ ππ S A π A 26. π₯ = __________ π¦ = __________ S T π ππ L ππ ππ π ππ π C π ππ N E π A 27. π₯ = __________ π¦ = __________ D π π π M π+π C I π π S Solve each of the following. 28. Measures (6): The sum of the measures of the interior angles of a hexagon is 720°. The measures of the angles of a particular hexagon are in the ratio 4: 5: 5: 8: 9: 9. What are the measures of these angles? 29. Measures (2): The ratio of the measure of two complementary angles is 4: 5. What are the measures of the angles? REVIEW PROBLEMS Solve for βπβ in each of the following. 30. π₯ = __________ π₯ + 6 5π₯ = 3 9 31. π₯ = __________ 2π₯ β 7 12 β 7π₯ = 9 6 Set up a proportion and solve. 32. __________ For field trips, the Brighton School requires that the teacher to student ratio be at least 2: 15. If there are 45 students on a field trip, what is the least number of teachers needed to supervise? 33. __________ Recall that the slope of a line is a ratio of the rise to the run. If a line has a slope of 3 , and you have chosen two points on the line that have 5 a rise of 15, what is the run? Find the correct answer for each of the following. Clearly circle your answers. Work must be shown in order to receive credit. 34. Which of the following statements is true? A. If two figures are similar, then they are congruent. B. If two figures are congruent, then they are similar. C. If two figures are similar, then their corresponding sides have the same length. D. Not Here 35. The angles of a triangle are in the ratio of 3: 4: 5. What is the degree measure of the smallest angle of the triangle? 36. The copy machine in the math workroom can make a copy of a document every 3 seconds. How many copies can it make in 17 minutes? A. 1024 B. 340 C. 240 D. 51