Honors Geometry Exam Review January 2015


 Archibald Horn
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1 Class: Date: Honors Geometry Exam Review January 2015 Multiple Choice Identify the choice that best completes the statement or answers the question. 1. How many planes can be drawn through any three noncollinear points? a. 0 c. 2 b. 1 d. Use the figure below. 2. Which three points in the figure are collinear? a. A, B, D c. E, C, A b. A, B, C d. F, E, G. Name the intersection of the plane P and the plane that contains points B, C, and D. a. point B c. BD b. BC d. triangle BCD 4. Find the length of PQ. a cm c cm b. 46. cm d. 21. cm 5. Find y if B is between A and C, AB is 2y, BC is 6y, and AC is 48. a. 24 c. 6 b. 8 d Find the distance between P(2, 8) and Q(5, ). a. 9 c. 4 b. 18 d Find the coordinates of the midpoint of LB if L(8, 5) and B( 6, 2). Ê a. 1, 1 ˆ Ê c. 7, 1 ˆ Ë Á 2 Ë Á 2 Ê b. 2,1 1 ˆ Ê d. 7,1 1 ˆ Ë Á 2 Ë Á 2 1
2 Use the figure below. 8. What type of angle is ABC? a. acute angle c. right angle b. obtuse angle d. straight angle Use the figure below. 9. Find m FBD if FBD and DBE are complementary and m FBD is twice m DBE. a. 0 c. 60 b. 45 d Which pair of angles are supplementary? a. ABE, CBD c. ABC, CBD b. ABC, ABD d. ABC, EBD 11. Which angle is a vertical angle to ABE? a. DBE c. ABC b. CBD d. EBA 12. If m CBF = 6x + 18, find x so that CB BF. a. 90 c. 18 b. 45 d Find m ABC if m ABC = 4x + 9 and m EBD = 7x 9. a. 6 c. 45 b. d. 7 2
3 14. Make a conjecture about the next object in this sequence. a. c. b. d. 15. Given: n is a positive number. Conjecture: n is a negative number. Which of the following would be a counterexample? a. 10 c. 1 b. 4 d If p is true and q is false, what is the truth value of p and q? a. true c. 0 b. false d. 1 Use the truth table. p q q p q T T T F F T F F 17. Which would be the values in the q column? a. F F T T c. F T F T b. T T F F d. T F T F 18. Which would be the values in the p q column? a. F T F F c. T T F T b. F T T F d. T F T T 19. Identify the conclusion of the statement Jack will go to school if today is Monday. a. Jack will go to school c. today is Monday b. Jack will not go to school d. today is not Monday 20. Identify the inverse of the following statement. If x = 2, then x + = 5. a. If x + = 5, then x = 2. c. If x 2, then x + 5. b. If x + 5, then x 2. d. x = 2 and x + = Identify the contrapositive of the following statement. If x = 2, then x + = 5. a. If x + = 5, then x = 2. c. If x 2, then x + 5. b. If x + 5, then x 2. d. x = 2 and x + = 5.
4 22. Which law can be used to determine that statement () is a valid conclusion to statements (1) and (2)? (1) If an angle is acute, then it cannot be obtuse. (2) A is acute. () A cannot be obtuse. a. Law of Detachment c. Law of Converse b. Law of Syllogism d. Statement () does not follow. 2. Which law can be used to determine that statement () is a valid conclusion of statements (1) and (2)? (1) If a figure has 4 right angles, then the figure is a rectangle. (2) A rectangle has 2 pairs of parallel sides. () If a figure has 4 right angles, then the figure has 2 pair of parallel sides. a. Law of Detachment c. Law of Converse b. Law of Syllogism d. Statement () does not follow. 24. Choose the property that justifies the following statement. If x = 2 and x + y =, then 2 + y =. a. Reflexive c. Transitive b. Symmetric d. Substitution 25. Choose the property that justifies the statement m A = m A. a. Reflexive c. Transitive b. Symmetric d. Substitution 26. Choose the property that justifies the statement If GH FD, then FD GH. a. Reflexive c. Transitive b. Symmetric d. Definition of congruent segments 27. If XY = 6, YZ = 4, and XZ = 2, which point is between the other two? a. X c. Z b. Y d. cannot tell Use the figure below. 28. If m BFC = 70, find m EFD. a. 10 c. 5 b. 20 d If m AFB = 5x 10 and m BFC = x + 20, find x. a. 10 c b. 15 d. 2. 4
5 Use the figures below. 0. If ABC EFG, and m ABC = 72, find m GFH. a. 18 c. 90 b. 72 d If m ABJ = 28, ABC DBJ, find m JBC. a. 90 c. 45 b. 56 d. 4 Refer to the figure below. Identify the special name for each angle. 2. and 10 a. alternate exterior c. consecutive interior b. alternate interior d. corresponding. 9 and 1 a. alternate exterior c. consecutive interior b. alternate interior d. corresponding 4. Given p Ä q and m = 75, find m 5. a. 15 c. 105 b. 75 d Given p Ä q and m 10 = x 7 and m 1 = 4x 9, find x. a. 2 c. 16 b. 2 d Given 1 5, which postulate or theorem justifies that p Ä q? a. Corresponding Angles Postulate b. Consecutive Interior Angles Theorem c. Alternate Exterior Angles Theorem d. Alternate Interior Angles Theorem 7. If 12 14, which postulate or theorem justifies that p Ä q? a. Corresponding Angles Postulate b. Consecutive Interior Angles Theorem c. Alternate Exterior Angles Theorem d. Alternate Interior Angles Theorem 5
6 8. If p Ä q by the Consecutive Interior Angles Theorem, which angle pair must be supplementary? a. and 10 c. 8 and 1 b. and 8 d. 15 and If m 4 = 7x 20 and m 8 = 5x + 18, find x so that p Ä q. a. 19 c. 1 b. 1 d. 19 Determine the slope of the line that contains the given points. 40. P( 6, ), Q(12, 9) a. c. b. 1 d. 41. M( 8, 14), N(2, 11) a. 5 2 c. 2 5 b. 2 5 d What is the slope of a line parallel to the line containing ( 6, 6) and (9, 14)? 10 a. c. 4 4 b. d. undefined 4. Find the slope of a line perpendicular to the line containing ( 8, 10) and (0, 9). 1 a. 8 c. 8 b d Which is an equation of the line with slope 1 that contains ( 4, 7)? 2 a. y 7 = 1 2 (x + 4) c. y 7 = 4x b. y 7 = 1 2 (x 4) d. y + 7 = 1 (x + 4) Which is an equation of the line with xintercept 2 and yintercept 12? a. y = 6x + 12 c. y = 6x + 12 b. y = 2x + 12 d. y = 12x Which is an equation of the line containing (1, ) and (7, 15)? a. y = x + 8 c. y = x 6 b. y = x d. y = x What is the distance between parallel lines whose equations are y = 2x + 7 and y = 2x? a. 2 c. 2 5 b. 5 d
7 48. What is the length of the sides of this equilateral triangle? a. 42 c. 15 b. 0 d How would ABC with vertices A(4, 1), B(2, 1), and C( 2, 1) be classified based on its sides? a. equilateral c. scalene b. isosceles d. right Use the figure. 50. What is m 1? a. 40 c. 70 b. 50 d What is m? a. 40 c. 90 b. 70 d If DJL EGS, which segment in EGS corresponds to DL? a. EG c. GS b. ES d. GE 5. Which triangles are congruent in the figure? a. KLJ MNL c. JKL LMN b. JLK NLM d. JKL MNL 7
8 54. The kite MNQP is made of two congruent triangles. In the kite, m N = 50 and m P = 100. What is the measure of M? a. 25 c. 60 b. 50 d The coordinates of the vertices of CDE are C(, 1), D( 1, 4), and E( 6, 4). A transformation applied to the CDE creates a congruent triangle C D E. The new coordinates of two vertices are D ( 1, 6) and E ( 6, 6). What are the coordinates of C? a. (, ) c. ( 1, 1) b. (1, ) d. ( 1, ) 56. If ABC is isosceles and AE FC, which theorem or postulate can be used to prove AEB CFB? a. SSS c. ASA b. SAS d. AAS 8
9 Use the proof. Given: DA Ä YN; DA YN Prove: NDY DNA Statements Reasons 1. DA Ä YN 1. Given 2. ADN YND 2. Alt. int. s are.. DA YN. Given 4. DN DN 4. Reflexive Property 5. NDY DNA NDY DNA What is the reason for statement 5? a. ASA c. SAS b. AAS d. SSS 58. What is the reason for statement 6? a. Alt. int. s are. c. Corr. angles are. b. CPCTC d. Isosceles Triangle Theorem 59. What is the classification of a triangle with vertices A(, ), B(6, 2), C(0, 2) by its sides? a. isosceles c. equilateral b. scalene d. right 60. What are the missing coordinates of the triangle? a. ( 2b, 0) c. ( c, 0) b. (0, 2b) d. (0, c) 61. What is the length of the sides of this equilateral triangle? a. 2.5 c. 15 b. 5 d. 20 9
10 Use the figure. 62. What is m 1? a. 120 c. 60 b. 90 d What is m 2? a. 120 c. 60 b. 90 d Which triangles are congruent in the figure? a. HMN HGN c. NMH NGH b. HMN NGH d. MNH HGN Use the proof. Given: EG IA; EGA IAG Prove: GEN AIN Statements Reasons 1. EG IA 1. Given 2. EGA IAG 2. Given. GA GA. Reflexive Property 4. EGA IAG GEN AIN What is the reason for statement 4? a. SSS c. SAS b. ASA d. AAS 66. What is the reason for statement 5? a. Alt. int. s are. c. Corr. angles are. b. Same Side Interior Angles d. CPCTC 10
11 Refer to the figure below. Identify the special name for each angle pair. 67. Given s Ä t and m 1 = 8x 4 and m 15 = 6x + 24, find x. a. 10 c. 20 b. 14 d If m 6 = 10x 6 and m 11 = 4x + 18, find x so that s Ä t. a. 2 c. 12 b. 4 d Find the slope of a line perpendicular to the line containing ( 2, 9) and (8, 6). a. 2 2 c. b Which is an equation of the line with xintercept 18 and a yintercept? a. y = 1 x + c. y = x b. y = 1 x + d. y = 6x + 6 d. 2 11
12 Honors Geometry Exam Review January 2015 Answer Section MULTIPLE CHOICE 1. ANS: B PTS: 1 NAT: NA 2. ANS: D PTS: 1 NAT: NA. ANS: B PTS: 1 NAT: NA 4. ANS: C PTS: 1 NAT: NA4 5. ANS: C PTS: 1 NAT: NA2 NA4 6. ANS: C PTS: 1 NAT: NA 7. ANS: A PTS: 1 NAT: NA 8. ANS: B PTS: 1 NAT: NA NA4 9. ANS: C PTS: 1 NAT: NA NA4 10. ANS: C PTS: 1 NAT: NA NA4 11. ANS: B PTS: 1 NAT: NA NA4 12. ANS: D PTS: 1 NAT: NA2 NA NA4 1. ANS: B PTS: 1 NAT: NA2 NA NA4 14. ANS: B PTS: 1 NAT: NA7 15. ANS: D PTS: 1 NAT: NA7 16. ANS: B PTS: 1 NAT: NA7 17. ANS: C PTS: 1 NAT: NA7 18. ANS: A PTS: 1 NAT: NA7 19. ANS: A PTS: 1 NAT: NA7 20. ANS: C PTS: 1 NAT: NA7 21. ANS: B PTS: 1 NAT: NA7 22. ANS: A PTS: 1 NAT: NA7 2. ANS: B PTS: 1 NAT: NA7 24. ANS: D PTS: 1 NAT: NA2 NA7 25. ANS: A PTS: 1 NAT: NA7 26. ANS: B PTS: 1 NAT: NA7 27. ANS: C PTS: 1 NAT: NA NA7 28. ANS: B PTS: 1 NAT: NA NA7 29. ANS: C PTS: 1 NAT: NA NA7 0. ANS: A PTS: 1 NAT: NA NA7 1. ANS: D PTS: 1 NAT: NA NA7 2. ANS: C PTS: 1 NAT: NA. ANS: D PTS: 1 NAT: NA 4. ANS: B PTS: 1 NAT: NA 5. ANS: D PTS: 1 NAT: NA2 NA 6. ANS: A PTS: 1 NAT: NA 7. ANS: C PTS: 1 NAT: NA 8. ANS: B PTS: 1 NAT: NA 9. ANS: D PTS: 1 NAT: NA2 NA 1
13 40. ANS: C PTS: 1 NAT: NA 41. ANS: A PTS: 1 NAT: NA 42. ANS: B PTS: 1 NAT: NA 4. ANS: D PTS: 1 NAT: NA 44. ANS: A PTS: 1 NAT: NA2 NA 45. ANS: A PTS: 1 NAT: NA2 NA 46. ANS: C PTS: 1 NAT: NA2 NA 47. ANS: C PTS: 1 NAT: NA 48. ANS: C PTS: 1 NAT: NA2 NA 49. ANS: C PTS: 1 NAT: NA 50. ANS: A PTS: 1 NAT: NA 51. ANS: D PTS: 1 NAT: NA 52. ANS: B PTS: 1 NAT: NA 5. ANS: D PTS: 1 NAT: NA 54. ANS: D PTS: 1 NAT: NA 55. ANS: A PTS: 1 NAT: NA 56. ANS: B PTS: 1 NAT: NA NA7 57. ANS: C PTS: 1 NAT: NA NA7 58. ANS: B PTS: 1 NAT: NA NA7 59. ANS: A PTS: 1 NAT: NA 60. ANS: A PTS: 1 NAT: NA 61. ANS: D PTS: 1 NAT: NA2 NA 62. ANS: D PTS: 1 NAT: NA 6. ANS: A PTS: 1 NAT: NA 64. ANS: B PTS: 1 NAT: NA 65. ANS: C PTS: 1 NAT: NA NA7 66. ANS: D PTS: 1 NAT: NA NA7 67. ANS: B PTS: 1 NAT: NA2 NA 68. ANS: C PTS: 1 NAT: NA2 NA 69. ANS: A PTS: 1 NAT: NA 70. ANS: A PTS: 1 NAT: NA2 NA 2
14 Honors Geometry Exam Review January 2015 [Answer Strip] B 14. A 22. B 1. B 2. A 0. D 15. D 1. B 8. D 24. B 16. A 25. D 2. B 26. B. C 27. C 2. C 4. C 9. C 17. D. C 10. A 18. B 4. C 5. C 6. B 11. D 12. A 19. C 20. B 28. C 29. D 5. A 6. B 1. A 7. B 21. C 7.
15 Honors Geometry Exam Review January 2015 [Answer Strip] B 8. C 48. D 54. D 9. C 40. C 49. D 62. A 6. A 41. A 55. B 64. B 42. A 50. B 56. C 57. B 58. D 51. A 59. D 4. B 52. A 60. D 5. A 44. A 45. C 46. C 47. D 61. C 65. D 66.
16 Honors Geometry Exam Review January 2015 [Answer Strip] B 67. C 68. A 69. A 70.
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