Practice - ibookfi.com
Transcription
Practice - ibookfi.com
Practice b. ACTIVITY 3.1 1. Explain why the following triangles are similar to one another. y 4n x 3n 4 z x 3 y The arrows indicate parallel lines. 7 15 + x 20 m 40° 32 m Y 30 m Q 2. x = 25m, y = 15m, z = 58° 3. Answers may vary. Check students’ rectangles. The sides should be in the ratio 7:4. ACTIVITY 3.3 ___ ___ ___ 6. Given the diagram with LD AE NT and segment measures as shown, determine the following measures. Show your work. R X 1. Corresponding sides are in proportion, and corresponding angles are congruent. 5m c. 2. The following triangles are similar. Determine the values of x, y, and z. Activity 3.2 y z - 18° 24 m 4. x ≈ 2.042 ft 60 cm 48 cm S S D E T 5a. SSS b. SAS 45 cm L 3. Sketch a figure that is similar but not congruent to a rectangle with length 14 in. and width 8 in. ACTIVITY 3.2 a. SL 4. Solve for x in the following figure. 22 ft. 8 cm A b. LD c. AA 16 cm N c. ET Activity 3.3 48 x 6a. ___ = _____ 60 x+8 x = 32; SL = 32 cm d. NT 7. Given CEL with measures as shown, determine x. Show your work. 4x + 1 48 x b. ___ = ___ 45 60 x = 36; LD = 36 cm 48 cm © 2010 College Board. All rights reserved. 18 ft. 7.5 ft. U C 5. State the theorem or postulate that allows you to determine similarity in the following pairs of triangles. 36 cm E 60 40 ___ c. ___ x = 16 x = 24; ET = 24 cm 42 cm x 45 60 ___ d. ___ x = 84 x = 63; NT = 63 cm L a. 12 cm 24 cm ACTIVITY 3.4 12 cm 8 cm 36 cm 4 cm 8. The ratio of similarity of corresponding sides of 2 . If the coordinates of STU and VWX is __ 3 S, T, and V are S (-4, 6), T(2, 6), and V(5, 7), determine a possible pair of coordinates for W. HIJ = H(8, -2), I(12, -2), J(-9, 8) LMN = L(-8, -8), M(-6, -8), N(-8, -1) Unit 3 • Similarity, Right Triangles, and Trigonometry x = ___ 12 7. ___ 42 36 x = 14 Activity 3.4 8. Possible coordinates: (14, 7) or (-4, 7) 9. Determine if HIJ ˜ LMN. 9. Corresponding side lengths are not in proportion so the triangles are not similar. 269 1/21/10 2:11:08 PM © 2010 College Board. All rights reserved. 269-271_SB_Geom_3-PRAC_SE.indd 269 UNIT 3 PRACTICE Activity 3.1 14 m z 7n W UNIT 3 Unit 3 • Similarity, Right Triangles, and Trigonometry 269 UNIT 3 Practice Activity 3.5 ACTIVITY 3.5 10a. PM = 6 in.; x2 + 82 = 102; x=6 10. Given RAM as shown. b. RP = 10_23_ in.; _68_ = _8x_; x = 10_2_ 3 c. RA = 13_13_ in.; 32 2 40 ___ + 64 = x2; ___ =x 3 3 ( ) Activity 3.6 11. __ 5√2 P a. Determine PM. b. Determine RP. c. Determine RA. 8 in R M 10 A ACTIVITY 3.6 11. Find the length of the hypotenuse of an isosceles right triangle with leg length 5 centimeters. Give the exact answer. 18. The perimeter of a square is 40 cm. Find the length of a diagonal. 19. Find the perimeter of a square, to the nearest tenth, if the length of its diagonal is 14 inches. 20. Find d and e. 60° cm 13. 30 inches 14a. right b. acute c. not a triangle d. obtuse __ __ 15. AB = √2 ; BC =7√2 ; AC = 10; AB + BC >10 so a triangle exists. AC 2 = AB 2 + BC 2 so the triangle is a right triangle. Activity 3.7 16. a = 3; b = __ e 8 12. Find the length of the altitude drawn from the vertex of an isosceles triangle with side lengths 13 in., 13 in., and 24 in. 12. 5 inches e. right 17. The measure of each leg of an isosceles right triangle is 5. Find the measure of the hypotenuse. d 13. An isosceles trapezoid has bases that are 7 inches and 13 inches long. The height of the trapezoid is 4 inches. Find the perimeter of the trapezoid. 21. The longer leg of a 30°– 60°– 90° triangle is 6 inches. What is the length of the hypotenuse? 14. Tell whether a triangle can be formed having the following side lengths. If a triangle can be formed, tell whether it is right, acute, or obtuse. 22. The length of an altitude of an equilateral triangle __ is 2 √3 inches. Find the length of a side of the triangle. a. b. c. d. e. 9, 40, 41 4, 5, 6 5, 12, 18 9, 9, 13 27, 36, 45 23. One side of an equilateral triangle is 8 cm. Find the length of the altitude. 24. The perimeter of an equilateral triangle is 36 inches. Find the length of an altitude. 15. Use the given vertices to determine whether ABC is a right triangle. Explain your reasoning and show the calculations that led to your answer. A(2, 7) B(3, 6) C(–4, –1) 25. Find the perimeter of the trapezoid. © 2010 College Board. All rights reserved. UNIT 3 PRACTICE Continued 18 cm 6 cm 60° __ 3√2 ACTIVITY 3.7 26. Find the perimeter of PQR. 16. Find a and b. 17. 5√2 R __ 18. 10√2 cm 19. 39.6 in. __ 60° b a 10 √ 3 20. d = 8√3 ; e = 16 __ 45° 12 __ inches, or 4√3 inches 21. ___ √3 P 30° Q 3 22. 4 inches __ 23. 4√3 cm __ 24. 6√3 in. 25. 54 cm 270 SpringBoard® Mathematics with Meaning™ Geometry __ __ 27. a = 3√6 ; b = 269-271_SB_Geom_3-PRAC_SE.indd 270 __ 6√2 270 SpringBoard® Mathematics with Meaning™ Geometry 1/21/10 2:11:11 P2 © 2010 College Board. All rights reserved. 26. 60 + 20√3 Practice b 6 a 12 ACTIVITY 3.8 28. Draw RST with right angle S. Identify the hypotenuse, adjacent leg, and opposite leg for ∠T. c. 0.306 15 30a. ___ 17 15 b. ___ 8 Q a. cos 49° b. sin 75° c. tan 17° 30. Using ABC below, write a ratio for the following. R 17 c. ___ 8 10 y 17 b. 0.966 N x 35. Find x and y. Round to the nearest tenth. 29. Use your calculator to evaluate the following. Round to 3 decimal places. A 29a. 0.656 y 36° M 60° 31. D__ P x √3 32a. ___ 2 36. Find each of the following using the given triangle. Round to the nearest tenth. B 15 31. In the diagram below, which trigonometric ratio 4? corresponds to __ 5 E © 2010 College Board. All rights reserved. 5 D a. cos E b. sin D F c. tan D d. cos D 32. Label the 30°– 60°– 90° triangle shown below with hypotenuse length 8 cm and label side lengths. Use your triangle to find the exact value of each ratio. Simplify all radicals. a. b. c. d. e. f. cos 30° sin 30° tan 30° sin 60° cos 60° tan 60° 70° c. AC B C 7.2 38. A ramp at the loading dock of an automobile manufacturing plant makes a 29° angle with the ground. The bottom end of the ramp is 30 meters from the building. a. Draw and label a diagram to illustrate the situation. b. Set up and solve an equation to find the length of the ramp. Round to tenths. 30° __ √3 c. ___ 3 √3 d. ___ 2 e. _12_ f. √3 __ 33. cos T = _35_; tan T = _43_ b. AB 37. A kite string is 200 meters long. Find the height of the kite if the string makes an angle of 38° with the ground. 3 4 a. m∠C b. _12_ __ A C ___ 28. hypotenuse: RT ; opposite ___ ___ leg: RS ; adjacent leg: ST O 30° 45° UNIT 3 PRACTICE Continued Activity 3.8 34. Find x and y. Round to the nearest tenth. 27. Find a and b. a. cos B. b. tan A c. csc B UNIT 3 39. In an isosceles triangle, the base is 32 cm long and the base angles are 56°. How long are the legs? 34. x = 9.7; y = 7.1 35. x = 11.5; y = 5.8 36a. 20° b. AB = 2.6 c. AC = 7.7 37. 123.1 meters 38a. r 29° 30 m b. r = 34.3 meters 39. 28.6 cm 4 ; find 33. In RST with right angle R, if sin T = __ 5 cos T and tan T. Unit 3 • Similarity, Right Triangles, and Trigonometry 1/21/10 2:11:13 PM © 2010 College Board. All rights reserved. 269-271_SB_Geom_3-PRAC_SE.indd 271 PM 271 Unit 3 • Similarity, Right Triangles, and Trigonometry 271