Geometry Regular Midterm Exam Review (Chapter 1, 2, 3, 4, 7, 9) Name: Date: Mod: Use the figure at the right for #1-4 1. What is another name for plane P? A. plane AE B. plane A C. plane BAD D. plane BAC 2. Which segment is on line n? A. AD B. BC C. D. BE 3. Name three collinear points. A. A, D, N B. M, A, E C. C, A, B D. P, B, C 4. Name the intersection of plane P and line m? A. line n B. point A C. AC D. AE 5. What is the measure of RT? A. 5 B. 16 C. 26 D. 40 6. X is the midpoint of WY. Find WX. A. 1 B. 6 C. 4 D. 12
Use the figure at the right for #7-8 7. Which term describes PMQ? A. obtuse B. straight C. right D. acute 8. What is m PMN? A. 22 B. 90 C. 68 D. 112 9. bisects CAD. m CAB = (4x 2) and BAD = (3x +6). Find CAD. Draw the picture. A. 60 o B. 8 o C. 12 D. 30 o 10. Two angles are supplementary. If m 1 = 67, what is m 2? 11. Find the measure of the complement of T, where m T = 49.3. 12. Given GH with endpoints G (-11, 4) and H (-1, -9), what are the coordinates of the midpoint of GH? A. (-12, -5) B. (-6, -2.5) C. (-10, 13) D. (-5, 6.5) 13. M is the midpoint of RS. R has coordinates (-12, 4) and M has coordinates (1, -2). What are the coordinates of S? A. (-5.5, -1) B. (-11, 2) C. (13, 6) D. (14, -8)
14. What is the distance from M (-1, 6) to N (11, 1)? A. 12 units B. 149 units C. 13 units D. 169 units Use the figure at the right for #15-17 15. Classify EH and DH A. skew B. parallel C. perpendicular D. none of these 16. How many segments are skew to AE? A. 1 B. 2 C. 3 D. 4 17. Classify DC and HG A. skew B. parallel C. perpendicular D. none of these Use the figure at the right for #18-19 18. Which are alternate interior angles? A. 1 & 3 B. 1 & 8 C. 3 & 6 D. 6 & 7 19. Which statement is true? A. 1 and 2 are alternate interior angles. B. 1 and 3 are corresponding angles. C. 3 and 6 are alternate exterior angles. D. 3 and 7 are same-side interior angles. 20. Which correctly completes the sentence? If two parallel lines are cut by a transversal, then the two pairs of alternate interior angles are. A. supplementary B. complementary C. corresponding D. congruent
21. What type of angle is 1? A. acute B. right C. obtuse D. straight 22. Given, what is the value of x? A. 6 B. 9 C. 72 D. 108 Use the figure at the right for #23-24 23. Which information proves that r s? A. 1 3 B. 4 5 C. 4 6 D. 5 6 24. If m 3 = (4x + 20) and m 5 = (6x + 10), what value of x proves that r s? A. 5 B. 15 C. 40 D. 100 25. If a transversal is perpendicular to one of two parallel lines, how many different angle measures are formed? A. 1 B. 3 C. 4 D. 8 26. Classify the triangle. A. isosceles acute B. isosceles obtuse C. scalene acute D. scalene obtus
27. Which is NOT a correct classification for ABC? A. acute B. isosceles C. equiangular D. scalene 28. What is the length of side BC? *Use picture from #27. A. 8 B. 6 C. 10 D. 24 29. What is m KLM? A. 3 B. 22 C. 42 D. 64 30. Find CA. 31. Find a, b, and c. 32. What is the value of x? A. 12 B. 19.5 C. 18 D. 60 33. Find x
34. Find m A. 35. Find x. 36. What is the m U? A. 5 B. 15 C. 40 D. 120 37. Two congruent triangles have the following corresponding parts: RS UV, RT UW, and R U. Which is NOT necessarily a correct congruence statement? A. RST UVW B. STR VWU C. TRS VWU D. TRS WUV 38. KLM RST, m L = (3x + 15) and m S = (6x + 3). What is the value of x? A. 2 B. 4 C. 6 D. 27 Use the figure for both #39 and #40. 39. If AD = 5y + 7 and BC = 7y - 3, what must the value of y be to prove AED CEB by the SSS postulate? A. 2 B. 5 C. 17 D. 32 40. What postulate or theorem justifies the congruence statement ABE CDE? A. SSS B. ASA C. SAS D. AAS
41. What method proves the triangles are congruent? A. SSS B. SAS C. HL D. AAS 42. For these triangles, select the triangle congruence statement and the postulate or theorem that supports it. A. ABC DEC; SAS B. ABC DEC; AAS C. BAC CED; AAS D. BAC CED; SSS 43. What is the value of x? x 3 2x 4 12 8 A. 81 B. 9 C. 4.5 D. Not here 44. If 21x = 63y, what is the ratio of x to y expressed in simplest form? 1 3 3 21 A. B. C. D. 3 9 1 7 45. The ratio of a dog park s length to its width is 11 : 9. If the width of the field is 180 yards, what is the length of the field? If necessary, round to the nearest whole number. A. 147 feet B. 220 feet C. 1620 feet D. not here 46. Which similarity statement is true for rectangles JKLM and PQRS given that JK = 6, JM = 5, QR = 15, and PQ = 12.5? A. rectangle JKLM ~ rectangle PQRS B. rectangle JKLM ~ rectangle QRSP C. rectangle JKLM ~ rectangle RQPS D. rectangle JKLM ~ rectangle SRQP
47. JKL ~ MNO. The similarity ratio of JKL to MNO is 5 : 2. What is the length of MN? A. 6 B. 10.8 C. 14 D. 37.5 48. Which similarity postulate or theorem lets you conclude that ABC ~ CDE? A. AA B. SAS C. SSS D. Triangles are not similar 49. Verify PQR and PRS are similar. Write a similarity statement and name the shortcut you used. 50. Verify JKL and JMN are similar. Write a similarity statement and name the shortcut you used. 51. The ratio of angles in a triangle is 1 : 3 : 4. Find the measure of the largest angle.
52. What is ST? *Hint: Draw the triangles separately. A. 18.75 B. 20 C. 32.5 D. 45 53. What information guarantees that XY AC? A. XB = 20, BY = 25 B. XB = 24, BY = 30 C. XB = 25, BY = 20 D. XB = 32, BY = 40 54. A student who is 60 inches tall measured shadows to find the height of a tree. The student s shadow was 24 inches long and the shadow of the tree was 13 feet long. Which proportion should the student use to find the height of the tree in inches? 60 24 5 2 60 x 60 x A. B. C. D. 156 x 13 x 24 13 24 156 55. A blueprint uses a scale of 1.5 in. : 24 ft. If the actual room has a width of 36 ft and a length of 51 ft, how long is the room in blueprint? A. 3. 4 in B. 1 1. 16 in C. 1 2. 4 in D. 3 3. 16 in 56. Find EF to the nearest tenth.
57. Find x. 58. Given the perimeter of ABC = 12 feet, find perimeter of XYZ. 59. Given the area of ABC = 6 feet 2, find the area of XYZ. Setup a proportion and solve for the value of x. 60. 61.
62. Reflect the figure with the given vertices across x-axis. A(-4, 1), B (2, 4), C (3, -2) A B C 63. Translate the figure with the given vertices along the vector <2, 3>. A (-2, 1), B (4, 3), C (2, -2) A B C 64. Rotate the figure with the given vertices about the origin with a counterclockwise 90 angle of rotation. A (2, 3), B (-2, 1), C (1, -1) A B C 65. Does the figure have line symmetry? If yes, draw all lines. Does the figure have rotational symmetry? If yes, give the angle of rotation and order of symmetry. Angle Order
66. What transformation is shown? A. rotation B. reflection C. translation D. image 67. Given a point in the coordinate plane, the rule (x, y) <2, -3> translates the point in which direction? A. 2 units to the left and 3 units up B. 3 units to the left and 2 units down C. 3 units right and 2 units up D. 2 units to the right and 3 units down EXTENDED RESPONSE SECTION 68. Name the corresponding sides and angles in each of the two examples below. a) SUN TAN Congruent angles: Congruent sides: b) Congruent angles: Congruent sides: 69. Find the missing angle measures. m 1 = m 3 = m 2 = m 4 =
70. Find the missing angle measures. m 1 = m 3 = m 2 = m 4 = m 5 = 71. For each pair of conditional statements, decide which is true (one, none, or both). If either is false, justify your answer by providing a counterexample. If an angle is a straight angle, its measure is 180. Truth value: If an angle measures 180, then it is a straight angle. Truth value: Counterexample if either is false: If an animal has wings, then it can fly. If it can fly, then an animal has wings. Truth value: Truth value: Counterexample if either is false: 72. Why are the triangles similar? Find PV.
73. Given: bisects ABC; AB CB Prove: DAB DCB 74. Given : M is the midpoint of PQ and Prove: QR PS RS 75. What does CPCTC stand for? 76. What does it mean for 2 polygons to be congruent? 77. What does it mean for 2 polygons to be similar? 78. Can 2 polygons be both congruent and similar? Why or why not? Explain.