Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Analytic geometry wikipedia , lookup
Euclidean geometry wikipedia , lookup
Architectural drawing wikipedia , lookup
Rational trigonometry wikipedia , lookup
Dessin d'enfant wikipedia , lookup
Perspective (graphical) wikipedia , lookup
Plane of rotation wikipedia , lookup
Conic section wikipedia , lookup
Lie sphere geometry wikipedia , lookup
Cartesian coordinate system wikipedia , lookup
Projective plane wikipedia , lookup
Name: ______________________ Class: _________________ Date: _________ Geometry 1-1 to 1-4 Practice Problems Multiple Choice Identify the choice that best completes the statement or answers the question. ____ 1. How many planes can be drawn through any three non collinear points? a. 0 b. 1 c. 2 d. 3 d. F, E, G Use the figure below to answer the following questions. ____ 2. Which three points in the figure are collinear? a. ____ b. A, B, C c. E, C, A 3. Name the intersection of the plane P and the plane that contains points B, C, and D. a. ____ A, B, D point B b. ←⎯ ⎯ → BC c. BD d. ΔBCD d. 3 d. A, D, E 4. Suppose A and B are points. How many lines contain both A and B? a. 0 b. 1 c. 2 Use the figure below to answer the following questions. ____ 5. Which three points in the figure are collinear? a. C, D, F b. A, E, F c. 1 B, C, D ID: A Name: ______________________ ____ 6. Name the intersection of the plane that contains points A, B, and D and the plane P. a. ____ ID: A point D b. triangle BCD c. AD 4 b. 40 c. 56 c. n d. p c. d. H JDB Refer to Figure 1. Figure 1 8. Name a line that contains point J. a. b. ____ ←⎯ ⎯ → BD 7. Given A is between Y and Z and YA = 14x, AZ = 10x and YZ = 12x + 48, find AZ. a. ____ d. ←⎯ ⎯ → DB ←⎯ ⎯ → GF 9. Name the plane containing lines m and p. a. n b. GFC ____ 10. What is another name for line n? a. b. line JB ←⎯ ⎯ → DC ____ 11. What is another name for line m? a. line JG b. ←⎯⎯ ⎯ → JGB c. ←⎯ ⎯ → GF d. AC c. DB d. line JB c. d. K ____ 12. Name a line that contains point A. a. b. ←⎯ ⎯ → DC m 2 DB d. 96 Name: ______________________ ID: A ←⎯ ⎯ → ←⎯ ⎯ → ____ 13. Name a point NOT contained in AD or FG . a. K c. b. A d. ____ 14. Which is these is NOT a way to refer to line BD? a. b. ←⎯ → JB m c. d. H D ←⎯⎯ ⎯ → JDB line JD ____ 15. Name three points that are collinear. a. b. B, G, F C, D, H c. d. J, G, F J, D, G c. d. Q, L, M R, S, K ____ 16. Name three points that are collinear. a. b. M, L, R L, P, T 3 Name: ______________________ ID: A ____ 17. Lines a, b, and c are coplanar. Lines a and b intersect. Line c intersects only with line b. Draw and label a figure for the relationship. a. c. b. d. Refer to Figure 2. Figure 2 ____ 18. Name three collinear points. a. B, L, D b. C, L, B c. d. K, A, C D, F, G ____ 19. Name a point that is NOT coplanar with G, A, and B. a. K c. C b. D d. F 4 Name: ______________________ ID: A ____ 20. Name four points that are coplanar. a. G, D, L, B b. C, K, A, G c. d. L, A, C, G K, B, D, L ____ 21. Name an intersection of plane GFL and the plane that contains points A and C. a. line LC c. line AC b. C d. plane CAB ____ 22. Which plane(s) contain point K? a. plane AGC b. plane ADB, plane ALC c. d. plane CAG, plane ABD plane DBA ____ 23. Which three-dimensional figure matches this net? a. c. b. d. ____ 24. ____ two points are collinear. a. Any b. Sometimes 5 c. No Name: ______________________ ID: A ←⎯ ⎯ → ____ 25. Which diagram shows plane PQR and plane QRS intersecting only in QR ? a. c. b. d. ____ 26. “ Two points determine a line.” Which of the following best describes the statement above? a. b. theorem postulate c. d. formula undefined term ____ 27. Which of the following best defines an axiom? a. b. c. d. finding a pattern in specific cases and then writing a statement for the general case an unproven statement that is based on observations a rule that is accepted without proof a proven statement used in a proof Short Answer 28. If EF = 6 and EG = 21, find the value of FG. The drawing is not to scale. 29. If EF = 5x + 15, FG = 53, and EG = 143, find the value of x. The drawing is not to scale. 6 Name: ______________________ ID: A 30. If EF = 2x − 12, FG = 3x − 15, and EG = 23, find the values of x, EF, and FG. The drawing is not to scale. 31. If Z is the midpoint of RT, what are x, RZ, and RT? 32. Which point is the midpoint of AE? 33. If T is the midpoint of SU, what are ST, TU, and SU? 34. If m∠AOC = 85°, m∠BOC = 2x + 10, and m∠AOB = 4x − 15, find the degree measure of ∠BOC and ∠AOB. The diagram is not to scale. 35. If m∠EOF = 26 and m∠FOG = 38, then what is the measure of ∠EOG? The diagram is not to scale. 7 Name: ______________________ ID: A Refer to Figure 1. Figure 1 36. Name a point NOT contained in lines m, n, or p. 37. Name the intersection of lines m and n. 38. Does line p intersect line m or line n? Explain. Refer to Figure 2. Figure 2 39. How many planes are shown in the figure? 40. How many planes contain points B, C, and A? 41. Where could you add point M on plane LBD so that D, B, and M would be collinear? 42. How many planes contain points B, L, F, and D? 43. Name the intersection of plane KCG and a plane that contains points L and D. 8 Name: ______________________ ID: A Find the measurement of the segment. 44. PR = 18.8 mm, RS = 13.7 mm PS = ? 45. QT = 0.4 in., QV = 1.9 in. TV = ? 46. Find the value of the variable and GH if H is between G and I. GI = 5b + 1, HI = 4b − 5, HI = 7 Use the number line to find the measure. 47. PH 48. RK Measure the angle. 49. 9 Name: ______________________ ID: A 50. Measure the angle and classify it as right, acute, or obtuse. 51. ∠1 52. ∠FGB 53. What is a net for the figure below? 10 Name: ______________________ ID: A 54. Are O, N, and P collinear? If so, name the line on which they lie. 55. Name the plane represented by the front of the box. 56. Are points B, J, and C collinear or noncollinear? 57. Name the ray in the figure. ⎯⎯ → 58. Name the ray that is opposite BA . 59. Find AC. 11 Name: ______________________ ID: A 60. If T is the midpoint of SU, find the values of x and ST. The diagram is not to scale. 61. If m∠EOF = 26 and m∠FOG = 38, then what is the measure of ∠EOG? The diagram is not to scale. 62. If m∠BOC = 27 and m∠AOC = 47, then what is the measure of ∠AOB? The diagram is not to scale. Use the figure below to answer the following questions. 63. Name three points on plane P. 64. Name the intersection of planes P and N. 12 Name: ______________________ ID: A Use the figure below to answer the following questions. 65. What is another name for line m? 66. Name three points on plane B. 67. Name the intersection of planes A and B. 68. Name three non collinear points. 69. Find the length of DE. 70. Measure ∠ABC. Then classify ∠ABC as right, acute, or obtuse. Use the figure below to answer the following questions. ←⎯ ⎯ → ←⎯ ⎯ → 71. Name a line that is coplanar with AD and AB . 72. Find the value of y if AC = 3y + 5, CB = 4y – 1, AB = 9y – 12, and point C lies between A and B. 13 Name: ______________________ ID: A 73. Name four rays shown. 74. Describe a real-life example of two planes and their intersection. 75. On a number line, P has coordinate –47 and Q has coordinate 40. Find PQ. 76. Are BC and DE congruent? Explain. 77. What are three names for the angle? 14