Class: Date: Geometry Semester 2 Final Review Multiple Choice Identify the letter of the choice that best completes the statement or answers the question. 1. Each unit on the map represents 5 miles. What is the actual distance from Oceanfront to Seaside? a. 10 miles c. about 8 miles b. 50 miles d. about 40 miles 2. Which angles are corresponding angles? a. 8 and 16 c. 4 and 8 b. 7 and 8 d. none of these 1
3. Graph y = 1 5 x + 3. a. c. b. d. 4. Write an equation in point-slope form of the line through point J( 5, 6) with slope 4. a. y 6 = 4( x 5) c. y + 6 = 4( x 5) b. y 6 = 4( x + 5) d. y 6 = 4( x + 5) 5. Write an equation in slope-intercept form of the line through point P( 10, 1) with slope 5. a. y = 5x 49 c. y 10 = 5(x + 1) b. y 1 = 5(x + 10) d. y = 5x + 1 6. Which two lines are parallel? I. 5y = 3x 5 II. 5y = 1 3x III. 3y 2x = 1 a. I and II c. II and III b. I and III d. No two of the lines are parallel. 7. Write an equation for the line parallel to y = 7x + 15 that contains P(9, 6). a. x + 6 = 7(y 9) c. y 6 = 7(x 9) b. y + 6 = 7(x 9) d. y + 6 = 7(x 9) 16
8. Can you use the ASA Postulate, the AAS Theorem, or both to prove the triangles congruent? a. either ASA or AAS c. AAS only b. ASA only d. neither 9. Name the theorem or postulate that lets you immediately conclude ABD CBD. a. SAS b. ASA c. AAS d. none of these 10. The length of DE is shown. What other length can you determine for this diagram? a. EF = 12 c. DF = 24 b. DG = 12 d. No other length can be determined. 3
Short Answer 11. Find m 1 and m 3 in the kite. The diagram is not to scale. 12. A model is made of a car. The car is 9 feet long and the model is 6 inches long. What is the ratio of the length of the car to the length of the model? 13. Solve the proportion. 3y 8 12 = y 5 14. You want to produce a scale drawing of your living room, which is 24 ft by 15 ft. If you use a scale of 4 in. = 6 ft, what will be the dimensions of your scale drawing? 15. Given: PQ Ä BC. Find the length of AQ. The diagram is not drawn to scale. 16. What is the intersection of plane TUYX and plane VUYZ? 4
17. If EF = 2x 12, FG = 3x 15, and EG = 23, find the values of x, EF, and FG. The drawing is not to scale. 18. If m EOF = 26 and m FOG = 38, then what is the measure of EOG? The diagram is not to scale. 19. M is the midpoint of CF for the points C(3, 4) and F(9, 8). Find MF. 20. Line r is parallel to line t. Find m 5. The diagram is not to scale. 21. Find the value of the variable if m Ä l, m 1 = 2x + 44 and m 5 = 5x + 38. The diagram is not to scale. 22. Find the values of x and y. The diagram is not to scale. 5
23. Find the values of x, y, and z. The diagram is not to scale. 24. Find the missing angle measures. The diagram is not to scale. 25. Find m A. The diagram is not to scale. 26. State whether ABC and AED are congruent. Justify your answer. 6
27. Find the values of x and y. 28. B is the midpoint of AC, D is the midpoint of CE, and AE = 21. Find BD. The diagram is not to scale. 29. Points B, D, and F are midpoints of the sides of ACE. EC = 30 and DF = 23. Find AC. The diagram is not to scale. 7
30. Find the value of x. 31. Q is equidistant from the sides of TSR. Find the value of x. The diagram is not to scale. 32. Name a median for ABC. 8
33. What is the name of the segment inside the large triangle? 34. Name the second largest of the four angles named in the figure (not drawn to scale) if the side included by 1 and 2 is 11 cm, the side included by 2 and 3 is 16 cm, and the side included by 3 and 1 is 14 cm. 35. Find the values of the variables and the lengths of the sides of this kite. 36. ABCD is a parallelogram. If m DAB = 115, then m BCD =?. The diagram is not to scale. 9
37. LMNO is a parallelogram. If NM = x + 15 and OL = 3x + 5 find the value of x and then find NM and OL. 38. For the parallelogram, if m 2 = 5x 28 and m 4 = 3x 10, find m 3. The diagram is not to scale. 39. Find the values of the variables in the parallelogram. The diagram is not to scale. 40. Find the values of a and b.the diagram is not to scale. 10
41. Find the length of the leg. If your answer is not an integer, leave it in simplest radical form. 42. Find the value of the variable(s). If your answer is not an integer, leave it in simplest radical form. Not drawn to scale 43. Write the tangent ratios for P and Q. 44. Find the value of x. Round your answer to the nearest tenth. 11
Find the value of x to the nearest degree. 45. Find the value of x. Round the length to the nearest tenth. 46. Find the area of the trapezoid. Leave your answer in simplest radical form. 47. 12
48. Find the area of the rhombus. Leave your answer in simplest radical form. 49. Find the area of a regular hexagon with side length of 8 m. Round your answer to the nearest tenth. 50. Find the length of arc XPY. Leave your answer in terms of π. 51. Use formulas to find the lateral area and surface area of the given prism. Show your answer to the nearest whole number. 13
Find the surface area of the cylinder in terms of π. 52. 53. Find the slant height x of the pyramid shown to the nearest tenth. 54. Find the slant height of the cone to the nearest whole number. 14
Find the volume of the given prism. Round to the nearest tenth if necessary. 55. Find the volume of the cylinder in terms of π. 56. 57. Find the volume of the composite space figure to the nearest whole number. 15
Find the volume of the square pyramid shown. Round to the nearest tenth as necessary. 58. Find the volume of the cone shown as a decimal rounded to the nearest tenth. 59. Find the volume of the sphere shown. Give each answer rounded to the nearest cubic unit. 60. 16