Name: Class: Date: ID: A Geometry Midterm Study Guide 1. PR! "" is represented by which sketch? 2. Draw a labeled diagram for a line. 3. Name three points in the diagram that are not collinear. 5. If m#ioj = 22 and m#hoi = 25, then what is the measure of #HOJ? 6. m#jhi = (2x + 7) and m#ghi = (8x $ 2) and m#jhg = 65. Find m#jhi and m#ghi. 4. Which angle measures approximately 72? a. b. 7. Name the angle below in 3 different ways. c. d. 1 8. In the figure (not drawn to scale), MO " "! bisects #LMN, m#lmo = (13x $ 31), and m#nmo = (x + 53). Solve for x and find m#lmn. 16. "If I get a chance, I will succeed." In this conditional statement, the underlined portion is. 17. "If I am invited, then I will go." What is the underlined portion called in this conditional statement? True or False: 9. The measure of angle A is 98. Classify angle A as an acute, right, or obtuse angle. Complete the conditional statement to make a true statement. 10. If #R and #S are complementary and m#r = 35, then 11. If #G and #H are supplementary and m#h = 67, then. 12. Solve for x: 18. The converse of a true conditional statement is always true. 19. True biconditionals make good definitions. 20. Which of the following is an example of the Transitive Property? a. If y = x $ 4, then x $ 4 = y. b. x $ 3 = x $ 3 c. If x = $3, then x $ 4 = $3 $ 4. d. If x $ 3 = y and y = $4, then x $ 3 = $4. 21. If PQ = 3 and PQ + RS = 5, then 3 + RS = 5 is an example of the. 22. Name the property which justifies the following conclusion: Given: 18x = 288 Conclusion: x = 16 Identify the property that makes the statement true. 23. If XY = MN, then MN = XY. 24. Classify %PQR. 13. #1 and #2 form a linear pair. m#1=73. Find m#2. 14. Name a pair of vertical angles in the figure above. 15. Rewrite the statement in if-then form. Every triangle has three sides. 2
25. Find the value of x. 27. Find the measure of the interior angles to the nearest tenth. (Drawing is not to scale.) 26. Find the value of x. 28. The two triangle-shaped gardens are congruent. Find the missing side lengths and angle measures. 29. Identify the congruent triangles. How do you know they are congruent? 31. Refer to the figure shown. Are the following triangles congruent? If so write a congruence statment and the Congruence that justifies your answer. 30. What must be true in order for %ABC & %EDC by the SAS Congruence Postulate? 3 32. Would HL, ASA, SAS, AAS, or SSS be used to justify that the pair of triangles is congruent? 37. Solve for x given BD = 5 x + 4 and AE = 6x + 4. 2 Assume B is the midpoint of AC and D is the midpoint of CE. 33. 34. 38. For the triangle shown, VS = 5 and VQ = 6. Then PQ =. 35. 36. In a triangle, a segment connecting the midpoints of two sides of the triangle is called a. 39. Which side lengths allow you to construct a triangle? a. 2, 3, and 8 b. 4, 1, and 9 c. 7, 2, and 2 d. 6, 8, and 10 40. Two sides of a triangle have lengths 7 and 13. The third side has a length that is. a. greater than 6 and less than 13 b. less than 20 and greater than 6 c. greater than 20 d. less than 6 41. Identify the largest angle of %ABC. 4
3 42. If x $ 4 = 7, then x =. x 43. Solve: 11 26 = x 15 46. Two ladders are leaning against a wall at the same 50. How long is a string reaching from the top of a angle as shown. 13-ft pole to a point on the ground that is 7 ft from the base of the pole? 51. For the triangle shown below, the Pythagorean Theorem states that. Refer to Figure 1 for 55-62 44. Given that ED BA = EC, find BC to the nearest BC tenth. The figure is not drawn to scale. 52. Find the length of the leg of this right triangle. Give an approximation to 3 decimal places. Figure 1 45. Which triangle is NOT similar to any of the others? a. b. c. d. How far up the wall does the shorter ladder reach? 47. Triangles LMN and NWR are right triangles. 48. What is the length of NW? Determine whether the triangles are similar. If the are, write a similarity statement. 53. If EFGH is a rectangle, what is FH? 54. For each set of numbers, determine whether the numbers represent the lengths of the sides of an acute triangle, a right triangle, an obtuse triangle, or no triangle. a. 38, 25, 13 b. 3, 4, 7 c. 6, 9, 12 d. 3.2, 4.2, 5.2 55. Name a line that contains point J. 56. Name a point NOT contained in lines m, n, or p. 57. Name the plane containing lines m and p. 58. What is another name for line n? 59. Name the intersection of lines m and n. 60. Does line p intersect line m or line n? Explain. 61. Name a line that contains point A. 62. Which of these is NOT a way to refer to line BD? a. '" JB! b. m c. '" JDB "! d. line JD 49. What value of x will make the two triangles similar? 5 6
Refer to Figure 2 for 63-67. Measure the angle. 71. Figure 2 72. 63. How many planes are shown in the figure? 64. How many planes contain points B, C, and A? 65. Name three collinear points. 66. Name four points that are coplanar. 67. Which plane(s) contain point K? Find the measurement of the segment. 68. PR = 18.8 mm, RS = 13.7 mm Find each measure. PS =? 73. m#1, m#2, m#3 Use the number line to find the measure. 69. PH 70. RK 7 74. m#1, m#2, m#3 75. Find m#k. 76. For these triangles, select the triangle congruence statement and the postulate or theorem that supports it. 8
77. Given: EC = 3AE, DB = 3AD Prove: %ABC ( %ADE Complete the proof. Proof: Statements Reasons 1. EC = 3AE, DB = 3AD 1. Given 2. AC = EC + AE, AB = DB + AD 2. Segment Addition Postulate 3. [1] 3. Substitution Property 4. AC = 4AE, AB = 4AD 4. Simplify. 5. AC AE 6. AC = 4, AB AD = 4 5. Division Property of Equality AE = AB AD 6. [2] 7. #A & #A 7. [3] 8. %ABC ( %ADE 8. SAS Similarity, steps 6 and 7 9