Class: Date: Honors Geometry Final REVIEW Short Answer 1. Find the lateral area of a cone if the height is 17 centimeters and the slant height is 19 centimeters. Use 3.14 for!. Round to the nearest tenth if necessary. 2. There are 84 boys in a freshman class of 146 students. Find the ratio of boys to girls. Identify the similar triangles. Find x. 3. 4. Determine whether QS Ä PT. Justify your answer. PQ = 18, QR = 6, RS = 12, ST = 36 1
Find x. Assume that any segment that appears to be tangent is tangent. 5. 6. 7. Lynn is standing at horizontal ground level with the base of the Sears Tower in Chicago. The angle formed by the ground and the line segment from her position to the top of the building is 15.7. The height of the Sears Tower is 1450 feet. Find her distance from the Sears Tower to the nearest foot. 2
8. Find x. Assume that segments that appear tangent are tangent. Find the area of the shaded region. Round answers to the nearest tenth. Assume all inscribed polygons are regular. 9. 10. Find the area of a circle having a circumference of 34!. Round to the nearest tenth. Use 3.14 for pi. 3
Each pair of polygons is similar. Write a similarity statement, and find x, the measures of the indicated sides, and the scale factor. 11. CB and AB Find the perimeter of the given triangle. 12. ABC, if ABC " PQR, BC = 6, QR = 11, PQ = 9, and PR = 13 13. ABC, if ABC " PQR, perimeter of PQR = 36, AC = 12, PR = 6 14. A baseball player made six hits in nine innings. What is the ratio of hits to innings? 4
Find the lateral area of each prism. Round to the nearest tenth if necessary. 15. 16. The dimension labeled 11 is the height of the prism. 17. Baseballs and softballs come in different sizes for different types of leagues. If the diameter of a baseball is 3 inches and a softball has a diameter of 3.8 inches, find the difference between the volumes of the two balls. Use 3.14 for!. Round to the nearest tenth. 18. A bird watcher spied a woodpecker. The bird watcher is 40 yards lower than the woodpecker. The distance from the bird watcher to the woodpecker is 175 yards. What is the angle of elevation? 19. Find x and y. 5
Find the measure of the numbered angle. 20. 21. 22. 6
23. Use the diagram to find the measure of the given angle. 24. m#daf Find the volume of the pyramid. Round to the nearest tenth if necessary. 25. 7
26. Find x. Assume that segments that appear tangent are tangent. Find x and the measures of the indicated parts. 27. BD and CE BD = 4x CE = 2x + 2 28. BC and AC 29. In ñd, AB $ CB and m arc CE = 44. Find m#bce. 8
30. Find the length of AE if BD Ä AE and BD is a midsegment of %ACE. 31. In ña, AC $ AF and AE = 45. Find meg. Find the volume of the cylinder. Use 3.14 for!. Round to the nearest tenth. 32. 9
33. In %DEF, given the lengths of the sides, find the measure of the stated angle to the nearest degree. d = 14.7, e = 21.3, f = 24.3; m#f Find the area of the figure. Round to the nearest tenth if necessary. 34. 35. 36. 10
37. 38. 39. Find x, y, and z. 11
40. Luna created a trash can in the shape of a triangular prism. The sides of the triangle are 1.6 feet, 2.3 feet, and 1.2 feet. Find the measures of the angles of the triangle to the nearest tenth. 41. Find x and y. 42. Each side of the square base of a regular pyramid is 9.9 centimeters. The sides rise at an angle of 55. Find the lateral area of the pyramid. Round to the nearest tenth. 43. Use the number line below to determine the ratio of BC to GK. 44. In ñu, TS = 15, UQ = US. Find mpr. 12
45. If m#1 = 7x + 5, m#2 = 10x, find m#1. Find x. Round to the nearest tenth if necessary. Assume that segments that appear to be tangent are tangent. 46. Solve each proportion. 47. 2 43 = j 13 48. Find the magnitude and direction of for the given coordinates. Round to the nearest tenth. C(6, 1), D(&5, & 4) 13
Find the surface area of the regular pyramid. Round to the nearest tenth if necessary. 49. Determine whether each pair of triangles is similar. Justify your answer. 50. Use the diagram to find the measure of the given angle. 51. #PRQ 52. A space shuttle is one kilometer above sea level when it begins to climb at a constant angle of 3 for the next 80 ground kilometers. About how far above sea level is the space shuttle after its climb? 14
Find the volume of the prism. Round to the nearest tenth if necessary. 53. 54. Quadrilateral ABCD is inscribed in ñz such that AB Ä DC and m#bzc = 76. Find m#dca. 55. Find the exact circumference of the circle. 15
Find the volume of the cone. Use 3.14 for!. Round to the nearest tenth. 56. 57. Find the geometric mean between each pair of numbers. 196 and 324 58. Find the perimeter and area of the parallelogram. Round to the nearest tenth if necessary. Find x. Round to the nearest tenth if necessary. 59. 16
60. Find each measure using the given measures of %KLM. Round measures to the nearest tenth. 61. If m#l = 71.9, k = 74.5, and l = 75.3, find m#k. 62. The solid below is a composite of a cube and a square pyramid. The base of the solid is the base of the cube. Find the lateral area of the solid. Find the lateral area of a cylinder with the given measurements. Use 3.14 for pi and round your answer to the nearest tenth. 63. height: 7 feet diameter: 8 feet 17
64. Find the area of the figure. Round to the nearest tenth if necessary. 65. Find the measure of the BD. Find the area of the indicated sector(s). Then find the probability of spinning the color indicated if the diameter of the spinner is 12. 66. pink 18
67. Write an equation for a circle with a diameter that has endpoints at ( 3, 7) and ( 1, 5). Round to the nearest tenth if necessary. 68. Find ST if QC and SD are altitudes and RQP " RST. 69. Find x. Assume that segments that appear tangent are tangent. 70. Find the area of the figure. Round to the nearest tenth if necessary. 71. Find the measure of the angle to the nearest tenth of a degree. cos B = 0.1184 72. Pat was flying a kite when the string broke and the kite fell to the ground. Pat is 36 yards lower than the kite. The distance from Pat to the kite is 200 yards. What is the angle of elevation? 19
The radius, diameter, or circumference of a circle is given. Find the missing measures. Round to the nearest hundredth if necessary. 73. d = 22.5 mi, r =?, C =? 74. Zack, Rachel, and Maddie are unraveling a huge ball of yarn to see how long it is. As they move away from each other, they form a triangle. The distance from Zack to Rachel is 3 meters. The distance from Rachel to Maddie is 2.5 meters. The distance from Maddie to Zack is 4 meters. Find the measures of the three angles in the triangle. 75. The length of a diagonal of a square is 9 2 millimeters. Find the perimeter of the square. Determine whether %QRS is a right triangle for the given vertices. Explain. 76. Q( 6, 2), R(2, 5), S( 3, 6) 77. Find AB if BD and QS are altitudes and ABC " PQR. 78. In ño, EC and AB are diameters, and #BOD $ #DOE $ #EOF $ #FOA. Find m arc BC. 20
Honors Geometry Final REVIEW Answer Section SHORT ANSWER 1. 506.2 centimeters 2 2. 42:31 3. %ABC " %EDF; x = 3 4. yes, PQ QR = ST SR = 3 5. 15 6. 22 7. 5159 ft 8. 11 9. 29.3 units 2 10. 907.5 units 2 11. EFGH " BADC; x = 25.04; CB = 23.04; AB = 25.92; 3.6 12. 18 13. 72 14. 2:3 15. 612 units 2 16. 264 units 2 17. 14.6 in 3 18. 13.2 19. x = 45, y = 13.1 2 20. 90 21. 125 22. 90 23. 81 24. 130 25. 3584 cm 3 26. 11 27. x = 5, BD = 20, CE = 12 28. x = 6, BC = 10, AC = 12 29. 113 30. 7 31. 72 32. 1254.7 cm 3 33. 83 34. 86.9 units 2 35. 66.2 units 2 36. 116.3 units 2 37. 38.3 units 2 38. 26 units 2 1
39. x ' 12.6, y ' 53.3, z ' 56.3 40. 109.6, 41.0, 29.4 41. x = 11, y = 11 3 42. 170.9 centimeters 2 43. 1:4 44. 30 45. 40 46. 6 47. 26 43 48. 12.1, 204.4 49. 120.0 yd 2 50. yes; %EDF " %BCA by AA Similarity 51. 85 52. 5.2 km 53. 313.7 m 3 54. 38 55. 18! 2 yds 56. 75.4 m 3 57. 6 7 58. 52 yd; 124.7 yd 2 59. 2 60. 5 61. 70.2 62. 768 m 2 63. 175.8 ft 2 64. 360 mm 2 65. 2 30 66. 18.8 units 2, 0.17 67. (x + 2) 2 + (y & 6) 2 = 2 68. 7 69. 9 70. 174.9 ft 2 71. 83.2 72. 10.4 73. r = 11.25 mi, C = 70.69 mi 74. m#z = 38.6, m#r = 92.9, m#m = 48.5 75. 36 millimeters 76. yes; QR = 73, QS = 73, RS = 146 ; QR 2 + QS 2 = RS 2 77. 6 78. 90 2