Geometry Practice Midterm


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1 Class: Date: Geometry Practice Midterm If Z is the midpoint of RT, what are x, RZ, and RT? A. x = 19, RZ = 38, and RT = 76 C. x = 17, RZ = 76, and RT = 38 B. x = 17, RZ = 38, and RT = 76 D. x = 15, RZ = 32, and RT = Find the coordinates of the midpoint of the segment whose endpoints are H(9, 10) and K(3, 14). A. (6, 4) B. (6, 12) C. (12, 24) D. (3, 2) 3. Two angles whose sides are opposite rays are called angles. Two coplanar angles with a common side, a common vertex, and no common interior points are called angles. A. vertical; adjacent B. adjacent; vertical C. vertical; supplementary D. adjacent; complementary 4. Find the distance between points P(4, 6) and Q(1, 7) to the nearest tenth. A B. 4 C. 3.2 D Determine whether the conditional and its converse are both true. If both are true, combine them as a biconditional. If either is false, give a counterexample. If an angle is a right angle, its measure is 90. If an angle measure is 90, the angle is a right angle. A. One statement is false. If an angle measure is 90, the angle may be a vertical angle. B. One statement is false. If an angle is a right angle, its measure may be 180. C. Both statements are true. An angle is a right angle if (and only if) its measure is 90. D. Both statements are true. The measure of angle is 90 if (and only if) it is not a right angle. 1
2 6. Find the values of x and y. A. x = 8, y = 27 C. x = 48, y = 132 B. x = 15, y = 17 D. x = 27, y = 8 7. Line r is parallel to line t. Find m 6. The diagram is not to scale. A. 30 B. 130 C. 20 D Find the value of x for which l is parallel to m. The diagram is not to scale. A. 148 B. 165 C. 55 D. 32 2
3 9. Find the value of x. The diagram is not to scale. A. 36 B. 26 C. 16 D What is the slope of the line shown? A. B C. 9 7 D
4 11. What is the graph of y = 1 3 x 5? A. C. B. D. 12. Name the theorem or postulate that lets you immediately conclude ABD CBD. A. ASA B. SAS C. AAS D. none of these 4
5 13. What is the graph of 2x 6y = 12? A. C. B. D. 5
6 14. Justify the last two steps of the proof. Given: MN PO and MO PN Prove: MNO PON Proof: 1. MN PO 1. Given 2. MO PN 2. Given 3. NO ON 3.? 4. MNO PON 4.? A. Reflexive Property of ; SAS C. Reflexive Property of ; SSS B. Symmetric Property of ; SSS D. Symmetric Property of ; SAS 15. Which triangles are congruent by ASA? A. VTUand ABC C. HGFand TVU B. VTUand HGF D. none 6
7 16. What is the value of x? A. 72 B. 108 C. 126 D Find the values of x and y. A. x = 90, y = 56 C. x = 34, y = 56 B. x =56,y=34 D. x =90,y= If MNO PQR, which of the following can you NOT conclude as being true? A. MN PR B. M P C. NO QR D. N Q 7
8 19. Find the length of the midsegment. The diagram is not to scale. A. 28 B. 18 C. 14 D DF bisects EDG. Find the value of x. The diagram is not to scale. A. 7 B. 4 7 C. 70 D Q is equidistant from the sides of TSR. Find the value of x. The diagram is not to scale. A. 7 B. 23 C. 15 D. 30 8
9 22. Find the circumcenter of the triangle. A. ( 3 2, 1 2 ) B. ( 1, 1 2 ) C. (1 2, 3 2 ) D. (3 2, 2) 23. Find the length of AB, given that DB is a median of the triangle and AC = 44. A. 44 C. 22 B. 88 D. not enough information 9
10 24. In ACE, G is the centroid and BE = 9. Find BG and GE. A. BG = 4 1 2, GE = 41 2 C. BG =3, GE =6 B. BG =6, GE =3 D. BG = 2 1 4, GE = Name a median for PQR. A. PU B. PS C. QS D. RT 26. Name the ray in the figure. A. BA B. AB C. AB D. AB 27. If EF =4x +15,FG =39,andEG =110, find the value of x. The drawing is not to scale. A. x =56 C. x =14 B. x =16 D. x =2 10
11 28. Complete the statement. GDF? A. DGF C. EDF B. DEF D. DFE 29. Name an angle complementary to BOC. A. DOE B. BOE C. BOA D. COD 30. Name the Property of Congruence that justifies the statement: If MN LK,thenLK MN. A. Symmetric Property C. Reflexive Property B. Transitive Property D. none of these 31. Name the Property of Congruence that justifies this statement: If A Band B C, then A C. A. Transitive Property C. Reflexive Property B. Symmetric Property D. none of these 11
12 32. What is the value of x? A. 16 B. 120 C. 60 D. 16 Use the diagram to find the following. 33. What are three pairs of corresponding angles? A. angles 1 & 2, 3 & 8, and 4 & 7 C. angles 1 & 7, 2 & 4, and 6 & 7 B. angles 3 & 4, 7 & 8, and 1 & 6 D. angles 1 & 7, 8 & 6, and 2 & 4 12
13 34. What is the relationship between 4 and 5? A. corresponding angles C. alternate interior angles B. sameside interior angles D. alternate exterior angles 35. Find the value of x. The diagram is not to scale. Given: SRT STR, m SRT =28, m STU =2x A. 28 B. 30 C. 14 D
14 36. ABC? A. PMN B. NPM C. NMP D. MNP 37. What other information do you need in order to prove the triangles congruent using the SAS Congruence Postulate? A. BAC DAC C. CBA CDA B. AC BD D. AC BD 14
15 38. Supply the missing reasons to complete the proof. Given: Q T and QR TR Prove: PR SR Statement 1. Q Tand QR TR Reasons 1. Given 2. PRQ SRT 2. Vertical angles are congruent. 3. PRQ SRT 3.? 4.PR SR 4.? A. ASA; Substitution C. AAS; Corresp. parts of are. B. SAS; Corresp. parts of are. D. ASA; Corresp. parts of are. 39. Find the value of x. The diagram is not to scale. A. x =60 B. x =21 C. x =15 D. none of these 15
16 40. Find the value of x. A. 7 B C. 8 D Which diagram shows a point P an equal distance from points A, B, and C? A. C. B. D. 16
17 42. Name the point of concurrency of the angle bisectors. A. A B. B C. C D. not shown 17
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