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Review -- Chapter 7 Multiple Choice ____ 1. A baseball player made six hits in nine innings. What is the ratio of hits to innings? a. 2:3 b. 3:2 ____ ____ c. 2:5 d. 5:2 2. Solve the proportion to find the value of x: a. 17 c. 7 10 b. 10 7 d. 3 3 17 C a. b. because the corresponding angles are congruent. is not similar to because the corresponding angles are not congruent. c. because the ratio of the corresponding sides is proportional and the corresponding angles are congruent. d. is not similar to because the ratio of the corresponding sides is not proportional. D C a. b. c. d. 5.9 71° 3.5 41° B 55° 7.3 5. Find x and the measure of AB. Show your work. a. b. c. d. A 40 10 E 12 x 56° 40° F 4. The triangle shown below are similar. Write a similarity statement and find the value of x. D ____ 71° 27.14 E ____ A 16.1 3. Determine if the triangles are similar. Justify your answer. F B 33.58 ____ ____ 6. Find x and the measures of EB and ED. Show your work. a. c. b. d. 7. Find x and the measure of AS. Show your work a. b. ____ c. d. 8. Find the length of if and is a midsegment of y 7 6 E A 5 4 3 2 (–1.5, 1.5) D –7 –6 –5 –4 –3 –2 B (2, 1.5) 1 –1 –1 1 2 3 4 5 6 7 x –2 –3 a. 12.25 b. 7 C c. 49 d. 12.25 . Show your work. ____ 9. Find the perimeter of the given triangle by using the following information: Show your work. P 9 8 S T 10 a. 40.5 b. 18 ____ c. d. 45 50.625 Q 10. Find PS if : 15 R A P is an altitude of is an altitude of 12 Show your work. 10 16 Q B a. 7.5 b. 19.2 c. d. D S R C 4.62 19.5 ____ 11. The figure below shows nested right isosceles triangles such as that the vertices of each smaller triangle are the midpoints of the sides of the next larger triangle. If AB = 12, find HI. a. b. c. d. 3 e. ____ 12. In the figure below, a. 10 ____ 13. In a. b. below, if b. 8 is similar to c. . What is the length of d. 12 ? Show your work. e. , find the measure of AB. Show your work. c. d. e. 5 Short Answer 14. Determine whether the pair of triangles is similar. Justify your answer and show your work. 15. Given || a). Identify the similar triangles. Write a similarity statement. A b). Find the value of x. Show your work. 2x - 14 c) Find the measures of sides and . B x-5 7 D E C 17 16. A class of 36 students has male and female students in the ratio of 4:5. What is the number of male students in the class? Show your work. . 17. Find x and y. Show your work. 3 x– 6 15 +2 x 2y (2/5) y + 3 18. In the coordinate plane below, AB and CD are parallel and OC = 2OA. How long is AB? Show your work. B 32 A D 0 -24 C 19. a) Identify the similar triangles using a similarity statement. b) Find the value of x. Show your work. c) Find the measures of sides 20. The base and height of similar triangles are shown in the table below. Base 6 9 18 24 Height 10 15 30 40 a) Circle all of the following triangles that are similar to the triangles listed in the table. Show your work. 21 35 6 20 50 4 12 15 35 30 b) Draw 3 more triangles that are similar to the triangles in the table: c) What is the ratio of the base to the height for the triangles in the table? Review -- Chapter 7 Answer Section MULTIPLE CHOICE 1. ANS: A How many hits does the player have? How many innings did the player play? Simplify the ratio. Feedback A B C D Correct! This is the ratio of innings to hits. Do not add the number of innings and hits. How many innings are in the game? PTS: 1 DIF: Basic REF: Lesson 7-1 OBJ: 7-1.1 Write ratios. STA: G.9(B) TOP: Write ratios. KEY: Ratios 2. ANS: D Find the cross products. Multiply. Divide each side by the coefficient of the variable. Feedback A B C D Reverse the numerator and denominator. Check your cross multiplication. The left side of the proportion cannot be reduced before cross multiplying. Correct! PTS: 1 DIF: Average REF: Lesson 7-1 OBJ: 7-1.2 Use properties of proportions. STA: G.9(B) TOP: Use properties of proportions. KEY: Proportions 3. ANS: B Two polygons are similar if and only if their corresponding angles are congruent and the measures of their corresponding sides are proportional. Feedback A B C D In order for the triangles to be similar, the corresponding angles must be congruent and the ratio of corresponding sides must be proportional. Correct! Are the angles congruent? Check the ratio of the corresponding sides. PTS: STA: KEY: 4. ANS: 1 DIF: Basic REF: Lesson 7-2 G.2(B) | G.3(B) | G.4 | G.9(B) | G.11(A) | G.11(B) Similar Figures B OBJ: 7-2.1 Identify similar figures. TOP: Identify similar figures. Feedback A B C D Is AC the same length as EF? Correct! Check the ratio of the corresponding sides. Check the similarity statement. PTS: 1 DIF: Basic REF: Lesson 7-3 OBJ: 7-3.1 Identify similar triangles. STA: G.2(B) | G.3(B) | G.4 | G.9(B) | G.11(A) | G.11(B) | G.11(C) TOP: Identify similar triangles. KEY: Similar Triangles 5. ANS: A Determine the ratio of corresponding parts. Use the ratio to find the missing information. Feedback A B C D Correct! Which side is AB? Check your operations. Which side does the question ask you to find? PTS: 1 DIF: Average REF: Lesson 7-3 OBJ: 7-3.2 Use similar triangles to solve problems. STA: G.2(B) | G.3(B) | G.4 | G.9(B) | G.11(A) | G.11(B) | G.11(C) TOP: Use similar triangles to solve problems. KEY: Similar Triangles | Solve Problems 6. ANS: D Determine the ratio of corresponding parts. Use the ratio to find the missing information. Feedback A B C D Check your ratio. Check your ratio and the values of the triangle sides. Check the expressions for each side of the triangle. Correct! PTS: 1 DIF: Average REF: Lesson 7-3 OBJ: 7-3.2 Use similar triangles to solve problems. STA: G.2(B) | G.3(B) | G.4 | G.9(B) | G.11(A) | G.11(B) | G.11(C) TOP: Use similar triangles to solve problems. KEY: Similar Triangles | Solve Problems 7. ANS: A Determine the ratio of corresponding parts. Use the ratio to find the missing information. Feedback A B Correct! Check your ratios. C D Check your ratios. Which side is missing? PTS: 1 DIF: Average REF: Lesson 7-3 OBJ: 7-3.2 Use similar triangles to solve problems. STA: G.2(B) | G.3(B) | G.4 | G.9(B) | G.11(A) | G.11(B) | G.11(C) TOP: Use similar triangles to solve problems. KEY: Similar Triangles | Solve Problems 8. ANS: B A midsegment of a triangle is one-half the length of the third side. Feedback A B C D What is the distance formula? Correct! Remember to take the square root. This is the length of BD not AE. PTS: 1 DIF: Average REF: Lesson 7-4 OBJ: 7-4.2 Divide a segment into parts. STA: G.2(B) | G.3(B) | G.4 | G.9(B) | G.11(A) | G.11(B) TOP: Divide a segment into parts. KEY: Lines Segments | Divide Line Segments 9. ANS: A If two triangles are similar, then the perimeters are proportional to the measures of the corresponding sides. Feedback A B C D Correct! Interchange the numerator and the denominator on either side of the proportion. If two triangles are similar, then the perimeters are proportional to the measures of the corresponding sides. Check your proportion again. PTS: 1 DIF: Average REF: Lesson 7-5 OBJ: 7-5.1 Recognize and use proportional relationships of corresponding perimeters of similar triangles. TOP: Recognize and use proportional relationships of corresponding perimeters of similar triangles. 10. ANS: A If two triangles are similar, then the measures of the corresponding altitudes are proportional to the measures of the corresponding sides. Feedback A B C D Correct! Interchange the numerator and the denominator on either side of the proportion. Use the correct proportion. If two triangles are similar, then the measures of the corresponding altitudes are proportional to the measures of the corresponding sides. PTS: 1 DIF: Basic REF: Lesson 7-5 OBJ: 7-5.2 Recognize and use proportional relationships of corresponding angle bisectors, altitudes, and medians of similar triangles. TOP: Recognize and use proportional relationships of corresponding angle bisectors, altitudes, and medians of similar triangles. 11. ANS: C PTS: 1 TOP: Trigonometry 12. ANS: D PTS: 1 TOP: Triangles and Quadrilaterals 13. ANS: A PTS: 1 TOP: Triangles and Quadrilaterals SHORT ANSWER 14. ANS: Not enough information to prove similarity. Two polygons are similar if and only if their corresponding angles are congruent and the measures of their corresponding sides are proportional. PTS: 1 DIF: Average REF: Lesson 7-3 OBJ: 7-3.1 Identify similar triangles. STA: G.2(B) | G.3(B) | G.4 | G.9(B) | G.11(A) | G.11(B) | G.11(C) TOP: Identify similar triangles. KEY: Similar Triangles 15. ANS: ; AB = 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. PTS: 1 DIF: Basic TOP: Solve multi-step problems. 16. ANS: 16 REF: Lesson 7-3 OBJ: 7-3.3 Solve multi-step problems. REF: Lesson 7-1 OBJ: 7-1.3 Solve multi-step problems. REF: Lesson 7-4 OBJ: 7-4.3 Solve multi-step problems. Let x be the number of male students. PTS: 1 DIF: Basic TOP: Solve multi-step problems. 17. ANS: To find x: To find y: PTS: 1 DIF: Basic TOP: Solve multi-step problems. 18. ANS: 15 PTS: 1 19. ANS: 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. PTS: 1 DIF: Advanced TOP: Solve multi-step problems. REF: Lesson 7-3 OBJ: 7-3.3 Solve multi-step problems.