Geometry Spring Final Exam Review 1. Find the sum of the measures of the interior angles of a convex hexagon. 2. Find the value of x. 68 110 135 x 3. Find the values of x and y in the parallelogram when,, m, m. 4. parallelogram is formed by the supports that attach a basketball backboard and rim to the wall. The angles change as the basketball apparatus is taken out and put away. Find when. 5. Find the coordinates of the intersection of the diagonals of with vertices,,, and.
6. For what values of x and y is quadrilateral a parallelogram? 4y+20 8x 34 9x 40 6x 4 7. Find the measures of the numbered angles in rhombus QRST. R 4 60 S 3 Q 5 1 2 T 8. Find. M 27 16 N 9. ecide whether quadrilateral with vertices,,, and is a rectangle, rhombus, square, or parallelogram. y : 4 2 4 2 2 4 x 2 4 10. Quadrilateral is a kite. What conditions must be true?
11. In rectangle,,, and. Find the value of y. P 12. The badge shown is shaped like a regular nonagon. Find the measure of each interior angle of the badge. Then find the measure of each exterior angle. 13. lassify the special quadrilateral. 14. The cross section of a brilliant cut diamond is shown. Find the measures of and 15. Find the number of sides a regular polygon must have so each interior angle measure is 162. Justify your answer. 16. The triangles are similar. Find the value of x. 30 24 32 R 24 S x 40 T
17.. Find the length of altitude. 15 M 12 E N 5 18. You are going to build a new garage similar to the rectangular one you currently have. The current dimensions are 25 feet wide by 20 feet long. You need to stake and rope off where the concrete will be poured. If the new garage is going to have a width of 30 feet, how much rope are you going to need? 19.. The area of is given. Find the area of. E 60 12 F = 1200 sq in. 20. lumber mill needs one more tree cut down that is at least 29 feet long. The person cutting down the tree is 6 feet 2 inches tall. Using shadows to determine whether a tree is tall enough, the person stands next to the tree and measures the length of his shadow as 32 inches. What is the length (to the nearest tenth of a foot) of the tree s shadow that will allow the tree to be cut down? 21. Find the value of x. 22 x 21 11
22. State a similarity statement(s). P F 82 I 82 T M 23. Find the value of x that makes. T 36 48 2x + 6 40 R x + 18 S 25 24. You are checking your friend s work on this problem. Is the solution correct? If not, explain and correct the error. What value of x makes? Explain. 40 6x + 6 30 32 18 ecause,
25. n architect is designing a covered bridge to be placed over a ravine. In the diagram, and represent the sides of the ravine, represents the road surface of the bridge, and represents the roof covering the bridge. Would these measurements ensure the roof is parallel to the road surface of the bridge? Explain 14 ft 10 ft F G 35 ft 30 ft 26. n adventure company wants to run a zip line from the top of one building that is 130 feet tall to the top of another building that is 30 feet tall. The two buildings are 72 feet apart. Estimate the length (in feet) of the zip line. Round your answer to the nearest tenth. 27. In the diagram, 2 and 2. Find. Write your answer in simplest form. 28. In the diagram,. Find and. Write your answers in simplest form. 29. Gym members are instructed to lift their legs at a 30 angle during leg lifts. One member has legs that are 33 inches long. What is the height (in inches) of the member s feet during the leg lift? If necessary, round decimal answers to the nearest tenth.
30. Solar panels installed in a backyard have a cross section that is a right triangle. The diagram shows the approximate dimensions of this cross section. vertical support from the right angle to the ground is recommended. pproximate the length of the support to the nearest tenth of a foot. 13.6 ft 4.4 ft 14.3 ft 31. Find the geometric mean of 12 and 48. 32. Find the value(s) of the variable(s). If necessary, round decimal answers to the nearest tenth. 32 57 x y 33. Find the exact value of the variable y 16 12 34. car is traveling along a road that makes a 10 angle with the ground. Find the elevation of the car on a stretch of road that extends horizontally 86 meters. Round your answer to the nearest tenth. 10 86 m Not drawn to scale
35. parasailer is attached to a boat with a rope. While parasailing, the angle of depression to the boat is 25. When the parasailer is attached to the boat with a 300-foot rope, how high above the boat is he? Round your answer to the nearest tenth of a foot. 36. Solve the triangle. Round decimal answers to the nearest tenth. 18 29 35 37. Identify the similar triangles. Match the statement below with the set of segment lengths it describes. Use each set of segment lengths only once. a. 10, 7, 658 d. 6, 5, 119 b. 6, 6, 38 e. 7, 24, 25 c. 6, 7, 85 38. The segment lengths form a right triangle. 39. The segment lengths form an acute triangle. 40. The segment lengths form an obtuse triangle. 41. The segment lengths do not form a triangle. 42. The segment lengths form a Pythagorean triple.
43. In the diagram, each side of quadrilateral is tangent to. Find the perimeter of the quadrilateral when,,, and. E H J F G 44. Match the value of x.. x 5 4 45. In the diagram,,, and. Find the measure of each arc. S a. b. c. U N Q W 46. In the diagram, is a diameter of and. Find HP. K M N P J H
47. In the diagram, and. Find. S R Q 48. In the diagram,. Find. G E F H 49. In the diagram, line m is tangent to the circle and. Find. m 50. Find the value of x. E G (2x + 21) (5x 8) (4x + 74) 51. In the diagram,,,, and. Find the value of x. J M N L K
52. park downtown has a circular fountain with a walkway that runs tangent to the fountain. You want to find the radius of the fountain using indirect measurement. You stand on the walkway at a point 16 meters from where it meets the fountain. This point is represented by in the diagram below and is 9 meters from the edge of the fountain. Knowing is tangent to the circle, find the radius r of the fountain. 9 m 16 m E r r 53. Find the center and radius of the circle. Q R P V Use the diagram of circle Q to answer the questions. U T S 54. What word best describes? 55. What word best describes? 56. Find the diameter of if measures 31 and the arc length of is 9 centimeters. 9 cm R P 31 Q S
57. onvert 186 to radians. 58. Find the area of the kite. 6 cm 11 cm 1 cm 59. Find the volume of the prism. 4 m 3 m 4 m 11 m 60. Pyramid and Pyramid are similar. The volume of Pyramid is 141 square centimeters. Find the volume of Pyramid. 32 cm 8 cm Pyramid Pyramid
61. Find the surface area of the cone. 9 cm 4 cm 62. Find the volume of the composite solid. 8 m 7 m 6 m 63. snowball has a radius of 7 centimeters. What is the volume? 7 cm
64. In the diagram, is a regular triangle inscribed in. Find the area of triangle given M=5. M 65. Find the areas of sectors formed by? 86.4 4.1 cm 66. The diagram shows a block of processed cheddar cheese that has a mass of 227 grams. Find the density of processed cheddar cheese to the nearest hundredth of a gram per cubic centimeter. 67. The m is 10 centimeters. Find the circumference of. 114º 10 cm