GEOMETRY Teacher: Mrs. Flynn Topic: Similarity. Teacher: Mrs. Flynn Topic: Similarity

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1 GEOMETRY Teacher: Mrs. Flynn Topic: Similarity Name: Date: Teacher: Mrs. Flynn Topic: Similarity 1. A tree casts a shadow 24 feet long at the same time a man 6 feet tall casts a shadow 4 feet long. Find the number of feet in the height of the tree. 5. If a girl 1.2 meters tall casts a shadow 2 meters long, how many meters tall is a tree that casts a shadow 75 meters long at the same time? 2. A 10-foot flagpole casts a shadow of 15 feet on level ground. A 6-foot man is standing next to the flagpole. Find the number of feet in the length of the shadow cast by the man 6. The ratio of perimeters of two isosceles right triangles is 1 : 3. If the length of the hypotenuse of the larger triangle is 18, find the length of the hypotenuse of the smaller triangle. 3. A tree 24 feet tall casts a shadow 16 feet long at the same time a man 6 feet tall casts a shadow x feet long. What is the length of the man s shadow? A. 6 B. 5 C. 3 D The sides of a triangle have lengths 6, 8, and 11. What is the length of the longest side of a similar triangle whose perimeter is 75? 4. A tree casts a shadow 30 feet long at the same time that a boy 5 feet tall casts a shadow 3 feet long. Find the height, in feet, of the tree. 8. The ratio of the corresponding sides of two similar triangles is 7 : 5. Find the ratio of their perimeters. page 1

2 9. The sides of a triangle measure 4, 6, and 7. If the shortest side of a similar triangle is 12, what is the perimeter of the larger triangle? 13. In the accompanying diagram of triangle XYZ and triangle ABC, X = A and Y = B. If XY = 5, YZ = 12, and AB = 15, what is BC? 10. The lengths of the sides of a triangle are 5, 12, and 13. What is the length of the longest side of a similar triangle whose perimeter is 90? A. 13 B. 15 C. 36 D The corresponding altitudes of two similar triangles are 6 and 4. If the perimeter of the larger triangle is 18, what is the perimeter of the smaller triangle? 14. In the accompanying diagram, right triangle ABC is similar to right triangle RST with A = R. If AB = 6, AC = 9, and RS = 4, find RT. 12. In the accompanying diagram, ABC is similar to PQR, AC = 6, AB = BC = 12, and PR = 8. Find the perimeter of PQR. 15. The lengths of the sides of a triangle are 8, 15, and 17. If the longest side of a similar triangle is 51, what is the length of the shortest side? A. 32 B. 24 C. 16 D. 4 Teacher: Mrs. Flynn page 2 GEOMETRY

3 16. In the accompanying diagram, ABC is similar to DEF, A = D, and B = E. If AB = 3, BC = 12, DE = x + 2, and EF = 18, find the value of x. 19. In the accompanying diagram, BAE, CAD, B and E are right angles, AB = 3, BC = 4, and AD = 15. What is the length of DE? A. 5 B. 8 C. 9 D The sides of a triangle measures 6, 11, and 15. If the smallest side of a similar triangle measures 4, find the length of its longest side. 20. In the accompanying diagram, IHJ LKJ. If IH = 5, HJ = 2, and LK = 7, find KJ. 18. In the accompanying diagram, ABC is similar to DEF, A = D, and B = E. If AB = 6, DE = 8, and DF = 12, find AC. 21. The sides of a triangle measure 3, 5, and 7. If the smallest side of a similar triangle measures 9, find its longest side. Teacher: Mrs. Flynn page 3 GEOMETRY

4 22. The sides of a triangle are 3, 4, and 5. Find the length of the shortest side if a similar triangle whose longest side has length The accompanying diagram shows two similar triangles. Which proportion could be used to solve for x? A. x 24 = 9 15 B = 15 x 23. The lengths of the sides of a triangle are 7, 8, and 10. If the length of the longest side of a similar triangle is 25, what is the length of the shortest side of this triangle? C. 32 x = D = 15 x 26. In right triangle ABC, altitude CD is drawn to the hypotenuse. If CD = 10 and AD = 4, then DB equals A. 2.5 B. 14 C. 25 D In the accompanying diagram, triangle A is similar to triangle B. Find the value of n. 27. In right triangle ABC, m C = 90, D is a point on AB, and CD AB. If AB = 20 and AD = 5, the length of AC is A. 10 B. 25 C. 300 D. 4 Teacher: Mrs. Flynn page 4 GEOMETRY

5 28. In the accompanying diagram of right triangle RST, altitude TP is drawn to hypotenuse RS. If TP = 6 and RP is 5 less than PS, find the length of hypotenuse RS. [Only an algebraic solution will be accepted.] 31. In the accompanying diagram, the altitude to the hypotenuse of the right triangle divides the hypotenuse into two segments of lengths 3 and 12. What is the length of the altitude? 29. In the accompanying diagram of rectangle ABCD, DE is perpendicular to diagonal AC. If AE = 3 and EC = 9, what is the length of AD? 32. In right triangle ABC, altitude CD is drawn to hypotenuse AB. If AD = 5 and DB = 24, what is the length of CD? A. 120 B. 30 C D A. 27 B. 6 C. 5 D The accompanying diagram shows two cables of equal length supporting a pole. Both cables are 14 meters long, and they are anchored to points in the ground that are 14 meters apart. 30. In the accompanying diagram, ABC is a right triangle and CD is the altitude to hypotenuse AB. If AD = 4 and DB = 16, find the length of CD. What is the exact height of the pole, in meters? A. 7 B. 7 2 C. 7 3 D. 14 Teacher: Mrs. Flynn page 5 GEOMETRY

6 34. Next to each numeral, give a reason for each statement in the proof. Given: Prove: ABC, ACB is a right angle, and CD AB. AC BD = CD BC 35. In the accompanying diagram, right triangle DEF is similar to right triangle ABC. The measure of AC is 2 more than the measure of BC, the measure of EF is 3 less than the measure of BC, and DF = 4. Statements Reasons ACB is a right angle, CD (1) AB B = B (2) CDB is a right angle (3) CDB = ACB (4) ABC CBD (5) AC CD = BC BD (6) AC BD = CD BC (7) a) Find the measure of BC. b) Find the measure of AB. c) What is the ratio of the area of ABC to the area of DEF? 36. In the accompanying diagram of right triangle ABC, altitude CD is drawn to hypotenuse AB, CA = 6, and AB is 7 more than AD. a) Find AD to the nearest hundredth. b) Using the results from part a, find the length of altitude CD to the nearest tenth. Teacher: Mrs. Flynn page 6 GEOMETRY

7 37. In the accompanying diagram, ABC is similar to A B C, AB = 14.4, BC = 8, CA = 12, A B = x, and B C = 4. Find the value of x. Teacher: Mrs. Flynn page 7 GEOMETRY

8 Problem-Attic format version c EducAide Software Licensed for use by Dyl Bro Terms of Use at Teacher: Mrs. Flynn GEOMETRY Topic: Similarity 02/14/ D : D B D C C A B C C [proof] 35. 6; 10; 4 : ;

2. If two isosceles triangles have congruent vertex angles, then the triangles must be A. congruent B. right C. equilateral D.

1. If two angles of a triangle measure 56 and 68, the triangle is A. scalene B. isosceles C. obtuse D. right 2. If two isosceles triangles have congruent vertex angles, then the triangles must be A. congruent