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Pre-AP Geometry Review Chapter 7 1. Determine which of the following isosceles triangles are similar. Justify your answer. P A 8 4 55° Q 3 6 70° B J 4.5 6 8 C 4 6. Find CE. R S L CE = __________ 2 Identify the similar triangles, find x, and then find the measures of the indicated sides. T 1.5 70° 6 55° 1.5 K U ___________________________ 7. Use the following information to find the measure. Polygon P M 18 6 Q N S 80° 11 7.5 O 15 KM = ________ R NM = ________ 2. ratio of the perimeter of polygon PQRS to the perimeter of polygon MNOS 8. ________ 3. MN _______ 4. perimeter of quadrilateral MNOS ________ 5. scale factor of quadrilateral PQRS to quadrilateral MNOS ________ PQ = ________ QS = ________ 13. 9. D A 3 9 F 8 x+ 2 B D C 4 E A 24 C CF = ________ 30 27 CA = ________ 10. Find PS if medians, and are and P A B A) B) C) D) No; sides are not proportional. yes; by SSS Similarity yes; by SSS Similarity yes; by SSS Similarity S D B F 10 6 C Q R 14. The ratio of measures of the three sides of a triangle is 5:6:9. If the perimeter is 220 meter. Find the measures of the sides of the triangle. PS = ______________ Determine whether each pair of triangles is similar. Justify your answer. ________, ________, _______ 11. 15. Find DC. ________________________ 12. DC = _______ _____________________ 16. Look at the figure shown below. 19. On a blueprint, inch represents 16 feet. If a driveway is 40 feet long, what is its length, in inches, on the map? If MKJ ~ MNL, which of the following must be true? A) , because corresponding angles of similar triangles are congruent. B) ____________ 20. A machine mints coins at the rate of one coin per second. If it does this for 10 hours each day, approximately how many days will it take the machine to mint 360,000 coins? , because the ratios of the lengths of corresponding sides of similar triangles are equal. C) , because the ratios of the lengths of corresponding sides of similar triangles are equal. D) , because corresponding angles of similar triangles are congruent. A) B) C) D) 10 100 1000 10000 21. Find QR. 17. Find y. QR = __________ 22. Find CE. y = __________ 18. A tree casts a shadow that is 3 feet 3 inches long. A man is 6 feet tall and casts a shadow 1 foot long. How tall is the tree? A) B) C) D) 19 ft 5 in. 19 ft 6 in. 19 ft 7 in. 19 ft 8 in. CE = __________ 23. If KLM XYZ, find the perimeter of XYZ. 26. Find FG, if BC =10, BA = 20, CA= 16, DC = 2, DE = 2.5 and EF = 24 ____________ _________ 24. ABC BX. JKL with altitudes BX and KY. Find 27. Find x. BX = __________ 25. Find x. x = __________ Use the figure below. 28. Identify the similar triangles. _____________________ ___________ 29. Find MN. _________ 30. Triangle has vertices and 31. Given: Prove: . 32. Given : Prove: is a midsegment. and is the midsegment of . Verify that Pre-AP Geometry Review Chapter 7 Answer Section 1. The corresponding angles are congruent, and the measures of their corresponding sides are proportional. Two polygons are similar if and only if their corresponding angles are congruent and the measures of their corresponding sides are proportional. 2. 2:1 Calculate the perimeter of polygon PQRS and the perimeter of polygon MNOS. Then find their ratio. 3. 9 The corresponding sides of similar figures are proportional to the scale factor. 4. 33.5 Calculate the lengths of MN and OS. Then find the sum of the four sides of the quadrilateral MNOS. 5. The numerical ratio obtained by comparing the lengths of corresponding sides of similar figures is called the scale factor. 6. 26 7. If the two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar. The measures of the corresponding sides of similar triangles are proportional. 8. If the two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar. The measures of the corresponding sides of similar triangles are proportional. 9. If the two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar. The measures of the corresponding sides of similar triangles are proportional. 10. 13.5 If two triangles are similar, then the measures of the corresponding medians are proportional to the measures of the corresponding sides. 11. Not similar; SSA is not a valid similarity. Two polygons are similar if and only if their corresponding angles are congruent and the measures of their corresponding sides are proportional. 12. yes; by AA Similarity Two polygons are similar if and only if their corresponding angles are congruent and the measures of their corresponding sides are proportional. 13. C 14. 55, 66, 99 15. 16 An angle bisector in a triangle separates the opposite side into segments that have the same ratio as the other two sides. 16. C 17. 18. B 19. 20. 21. 22. 23. 24. A 56 25 45 19.2 25. 26. 27. 28. 29. 30. 31. 32. or 19.2 12 7.5 See solution See solution See solution 18.76