Geometry - Midterm Exam Review - Chapters 1, 2
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1 Geometry - Midterm Exam Review - Chapters 1, 2 1. Name three points in the diagram that are not collinear. 2. Describe what the notation stands for. Illustrate with a sketch. 3. Draw four points, A, B, C, and D, on a line so that and are opposite rays and and are the same ray. 4. Sketch the intersection of a line and a plane. 5. If RS = 44 and QS = 68, find QR. 6. Let be between and. Use the Segment Addition Postulate to solve for. = = = R, S, and T are collinear. S is between R and T. RS = 2w + 1, ST = w 1, and RT = 18. Use the Segment Addition Postulate to solve for w. Then determine the length of AB = x + 16, BC = 5x + 10, AC = Find AB and BC in the situation shown above. 9. a. Plot the following points in a coordinate plane: A ( 2, 2), B (3, 2), C ( 2, 4), D (3, 4), b. Is congruent to? Explain. c. Is there another pair of congruent segments? If so, name the segments and explain why they are congruent. 10. Find the distance between the points (1, 4) and ( 2, 1). 11. Find the midpoint of the segment with endpoints (9, 8) and (3, 5).
2 12. The distance between points A and B is. 13. T is the midpoint of. Which one of the following is not an appropriate statement? a. b. c. d. 14. Point S is between points R and T. P is the midpoint of. RT = 20 and PS = 4. Draw a sketch to show the relationship between the specified segments. Find ST. 15. The midpoint of is. One endpoint is. Find the coordinates of the other endpoint. 10 y J M x 10 BC = 7x 13, AB = 4x + 26, B is the midpoint of. 16. Find AB and BC in the situation shown above.
3 17. If and, then what is the measure of? 18. m JHI = ( ) and m GHI = ( ) and m JHG = 65. Find m JHI and m GHI. 19. Which does not name the angle below? a. DCE b. CDE c. ECD d. C 20. In the figure (not drawn to scale), bisects, and. Solve for x and find
4 21. Name. B C A O D E 22. and are opposite rays. bisects.. Draw a sketch and find. 23. Which figure below is not a polygon? a. b. c. d. 24. The figure below is an example of a(n). 25. Which figure below is not a convex polygon? a. b. c. d. 26. Complete the statement. A regular polygon is both and equiangular. 27. The lengths (in inches) of two sides of a regular octagon are represented by the expressions and. Find the length of a side of the octagon. 28. Sketch an equiangular convex hexagon.
5 29. Find the circumference of the circle. Use = Find the area. All lengths are in centimeters A wooden fence is to be built around a 50 m-by-62 m lot. How many meters of fencing will be needed? If the wood for the fence costs $47.75 per meter, what will the wood for the fence cost? 32. Find the area of a circle with radius 23 cm. Use 3.14 for. 33. A can of paint will cover 70 square feet. How many cans of paint are needed to paint a wall 5 feet high and 98 feet long? 34. If the pattern indicated below is continued, what would be the total number of cubes in the 8th stage of the pattern? 35. Give one counterexample that shows the conjecture is false. In a coordinate plane, if the y-coordinate of a point is positive, then the point is in the first quadrant. Use inductive reasoning to find the next two numbers in each pattern , 18, 20, 22,, 37. 2, 4, 8, 16,, 38. Rewrite the statement in if-then form. Every triangle has three sides.
6 True or False: A l D m G B J C H n F E is perpendicular to line n. 41. and are supplementary. 42. and are complementary. 43. is perpendicular to line m. 44. Points D, J, and F are collinear. 45. Write the inverse of the following statement. If a number is not even, then it is not divisible by two. In 46 47, from the given true statements, make a valid conclusion: 46. If Ahmed can get time off work, he will go to Belize. If Ahmed goes to Belize, Jake will go with him. Ahmed will get time off work. 47. If there is no more milk, Rita will go to the store. There is no more milk. 48. Rewrite the postulate in if-then form. "A line contains at least two points." 49. State the postulate indicated by the diagram Name the property which justifies the following conclusion: Given: Conclusion: 52. Name the property which justifies the following conclusion: Given: Conclusion:
7 In 53 56, identify the property that makes the statement true. 53. If XY = MN, then MN = XY. 54. If m P = m R and m R = m T, then m P = m T. 55. If MP = PQ and PQ = QR, then MP = QR. 56. If m 1 + m 2 = 25 and m 1 = 9, then. 57.Provide the reasons for each statement in the proof. Given: Prove: A B C D E 58.Provide the reasons for each statement in the proof. Given: Prove: A B C D E F
8 In 59 61, write a two-column proof. 59. Given:, is supplementary to, and is supplementary to Prove: 60. Given: bisects Prove: 61. Given: 4(x 2) = 3x +7 8 Prove: x = In the figure shown,. Which of the following statements is false? A D E B C a. b. c. d. 69. Solve for x. 70. are supplementary angles. are vertical angles. If what is
9 Geometry - Midterm Exam Review - Chapters 1, 2 Answer Section 1. Answers will vary. 2. A ray from R through S 3. Sketches vary. 4. Sketches vary = AB = 21, BC = a. See diagram below. b. Yes, because each has a length of 5. c. Yes. Sample answer: because each has a length of B ( 6, 13 )
10 15. ( 8, 7) 16. AB = 78, BC = m JHI = 19 and m GHI = B 20. 7, Sketches may vary. 23. A 24. heptagon 25. A 26. equilateral inches 28. Sample answer: in m, $10, Answers will vary. The point ( 4, 5) is not in the first quadrant , , If a figure is a triangle, then it has three sides. 39. True 40. True 41. True 42. True 43. False 44. False 45. False 46. False 47. If a number is even, then it is divisible by two. 48. Ahmed will go to Belize, and Jake will go with him. 49. Rita will go to the store. 50. If Isaiah walks the tightrope, he will get hurt. 51. If Joshua works on Sunday, he will not work on Wednesday.
11 52. Larinda will not get her allowance. 53. The catcher will take them to the pound. 54. Cinderella is the one. 55. If a figure is a line, then it contains at least two points. 56. A line contains at least two points. 57. Through any three noncollinear points there exists exactly one plane. 58. Substitution property of equality 59. Multiplication property of equality 60. Symmetric Property of Equality 61. Transitive Property of Equality 62. Transitive Property of Equality 63. Substitution Property of Equality B
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