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Class: Date: Geometry First Semester Exam 2013-14 1. T is the midpoint of PQ. Which one of the following is not an appropriate statement? a. PT = TQ c. PT TQ b. PT = TQ d. PT + TQ = PQ 2. Which angle measures approximately 72? a. c. b. d. 3. Which does not name the angle below? a. DCE b. CDE c. ECD d. C 4. Which is not a possible value for y in the figure below? a. 70 b. 115 c. 55 d. 160 1

5. Which figure below is not a polygon? a. b. c. d. 6. Which figure below is not a convex polygon? a. b. c. d. 7. Which one of the statements below is false? a. A circle is NOT a polygon. c. A decagon has 10 sides. b. An octagon has 8 angles. d. A pentagon has 9 angles. Use the formula for the area of a triangle (A = 1 bh) to find the value of the unknown variable. 2 8. Henry wants to use 48 feet of fencing to enclose part of his yard for a garden. Which of the figures described would use all 48 feet of fencing and enclose the largest area of Henry's yard? a. A rectangle with a length of 14 feet and a width of 10 feet b. A rectangle with a length of 16 feet and a width of 8 feet c. A square with a side length of 12 feet d. A circle with a radius of about 7.6 feet Make a scatter plot of the data. What conclusions can you make? 9. Number of TVs 3 2 2 1 3 1 2 1 Number of Plane Trips Last Year 2 6 1 3 4 2 3 4 a. As the number of TVs increase, the number of plane trips decrease. b. As the number of TVs decrease, the number of plane trips decrease. c. As the number of plane trips increase, the number of TVs increase. d. no relationship 2

10. The figure below represents which of the following statements? a. Two rays that are perpendicular b. A straight angle c. AB = AC d. Two lines that are perpendicular 11. Decide which one of the following statements is false. a. Three noncollinear points determine a plane. b. A line contains at least two points. c. Through any two distinct points there exists exactly one line. d. Any three points lie on a distinct line. 12. 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. 13. In the figure shown, m AED = 124. Which of the following statements is false? a. BEC and CED are adjacent angles. b. AEB and DEC are supplementary angles. c. m AEB = 56 d. m BEC = 124 3

14. In the figure, l Ä n and r is a transversal. Which of the following is not necessarily true? a. 8 2 c. 5 3 b. 2 6 d. 7 4 15. In the figure shown, HC Ä GD and m ABC = 100. Which of the following statements is false? a. m CBE = 80 b. m DEF = 80 c. DEB and CBE are corresponding angles. d. CBE and GEB are alternate interior angles. 4

16. Line m is parallel to line n and they are each intersected by the same two transversals. Which angle is NOT necessarily congruent to 4? a. 12 c. 7 b. 16 d. 15 17. Which best describes the relationship between the line that passes through (7, 1) and (10, 5) and the line that passes through ( 8, 5) and ( 5, 9)? a. same line b. perpendicular c. neither perpendicular nor parallel d. parallel 18. Which best describes the relationship between Line 1 and Line 2? Line 1 passes through Ê Ë 3, 6 Ê Ë Á 7, 11 ˆ Line 2 passes through Ê Ë 1, 8 Ê Ë Á 4, 4 ˆ a. perpendicular b. They are the same line. c. parallel d. neither perpendicular nor parallel 19. A line L 1 has slope 4 9. The line that passes through which of the following pairs of points is parallel to L 1? a. (6, 3) and (2, 6) c. ( 5, 2) and (6, 6) b. (12, 1) and (2, 8) d. ( 3, 2) and (6, 6) 5

20. Which graph below would match the situation described? A car is traveling at 44 mph slows to 21 mph in the first 5 seconds. It maintains that speed for the next 5 seconds, and then slows to a stop in the next five seconds. a. c. b. d. 21. Which best describes the relationship between the lines with equations 5x 8y = 4 and 30x 48y = 24? a. neither parallel nor perpendicular b. same line c. parallel d. perpendicular 6

22. The equation 2x 2y = 6 is graphed below. Which of the following graphs shows the result of changing the 2 in 2x 2y = 6 to 1? a. c. b. d. 23. A triangle has angle measures of 60, 60, and 60. Choose the term that describes the triangle. a. Equiangular b. Right c. Obtuse d. Scalene 24. Which pair of lengths can be two of the sides of an isosceles triangle which has a perimeter of 52 inches? a. 15 inches, 25 inches c. 12 inches, 22 inches b. 15 inches, 22 inches d. 16 inches, 21 inches 25. If ABC DEF, AB = 10 feet, m B = 27, and m F = 14, which of the following statements is false? a. AC = DF c. m E = 139 b. C F d. AB = DE 26. If MNO VWX, which statement is NOT true? a. NO VW c. MO VX b. O X d. N W 7

27. Determine which triangle is congruent to the given triangle. a. none of these c. b. d. 28. Refer to the figure shown. Which of the following statements is true? a. TUV XWV by ASA c. TUV WXV by SAS b. TUV VWX by SAS d. TUV WXV by SSS 8

29. In ABC, AB = 3x 2, BC = x + 4, and AC = 7. Also AB BC. Which term does NOT describe ABC? a. Equilateral b. Acute c. Isosceles d. Obtuse 30. Given: ABC DEF with AB BC. Which statement of congruence is not provable? a. ABC CBA b. DEF CBA c. ABC FDE d. ABC FED 31. Which picture shows a reflection of the flag? a. c. b. d. 32. Which graph represents a reflection in the x-axis? a. c. b. d. 9

33. A person facing east walks east 20 paces, turns, walks north 10 paces, turns, walks west 25 paces, turns, walks south 10 paces, turns, walks east 15 paces, and then stops. What one transformation could have produced the same final result in terms of the position of the person and the direction the person faces? a. reflection over the north-south axis b. rotation c. translation d. reflection over the east-west axis 34. Given: BC is the perpendicular bisector of KM. Which statement is true? 35. OE a. BLM, MLC, CLK, KLB are allright angles. b. CM = BM c. KBM is a right angle. d. C is the midpoint of KM bisects BOA, EA OA, and EB OB. Which statement is NOT true? a. AE BE c. OA OB b. AOE EAO d. AEO BEO 36. 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 37. Which of these lengths could be the sides of a triangle? a. 15 cm, 4 cm, 20 cm c. 11 cm, 5 cm, 16 cm b. 3 cm, 15 cm, 20 cm d. 5 cm, 12 cm, 16 cm 10

38. Given the triangles below, if ZY CB, XY AB, and m B > m Y, decide which statement is true. a. YZ > BC b. XZ < AC c. XY < AB d. AC < XZ 39. In PQR and EGF, PR EF, QR GF, PQ = 18 cm, EG = 24 cm, and m R = 65 o Which angle measure is reasonable for F? a. 55 b. 65 c. 70 d. 60 40. Which statement is false for the diagram? a. MN = NR b. LM = PR c. LN < NP d. LN > NP 41. Refer to the figure. Choose the correct statement. a. x < 10 c. x > 13 b. 10 < x < 13 d. x = 13 11

42. Refer to the figure below. Given: AB = AD, m 1 > m 2. Then,. a. BE > ED b. BE < ED c. AE = EC d. BE = ED 43. If P Q = R, which of the following is NOT true? S a. R S = P Q b. PS = RQ c. Q P = S R d. PR = SQ 44. If a b = c, then. d a + b a. = c + b b d b. ac = bd d. c. a + b = c + d b d a b = a + c b + d 45. The Community Recreation Center is developing plans for a new sports facility. Community members can submit suggestions for the new facility, along with basic scale drawings of their ideas. Rachel wants to include a new 11- by 24-meter tennis court in the athletic center. She is submitting a scale drawing on an 8.5- by 11-inch sheet of paper. Which scale should Rachel use to create as large a drawing as possible on the paper? 3 a. 8 in. = 1 m b. 3 4 in. = 1 m c. 1 8 in. = 1 m d. 7 16 in. = 1 m 46. Which triangle is NOT similar to any of the others? a. b. c. d. 47. One way to show that two triangles are similar is to show that. a. two angles of one are congruent to two angles of the other b. two sides of one are proportional to two sides of the other c. a side of one is congruent to a side of the other d. an angle of one is congruent to an angle of the other 12

48. If the corresponding sides of two triangles are proportional, then. a. the triangles are right triangles b. the triangles are similar c. corresponding side lengths are equal d. the triangles are congruent 49. If ABC ~ PBQ, then which of the following proportions is NOT true? a. AC PQ = CB QB b. AP PB = AC PQ c. AP PB = CQ QB d. PB AB = PQ AC In the figure below, ABC A' B ' C '. 50. Which statement is true of the transformation from ABC to A' B ' C '.? a. The measures of all corresponding angles change by a scale factor of 2. b. The measures of all corresponding angles change by a scale factor of 1 2. c. The lengths of all corresponding sides change by a scale factor of 2. d. The lengths of all corresponding sides change by a scale factor of 1 2. 13

Geometry First Semester Exam 2013-14 Answer Section 1. ANS: B PTS: 1 DIF: Level B REF: MGEH0006 STA: MI.MIGLC.MTH.06.9-12.G1.1.3 MI.MIGLC.MTH.06.9-12.G1.1.5 TOP: Lesson 1.3 Use Midpoint and Distance Formulas KEY: midpoint BLM: Comprehension 2. ANS: D PTS: 1 DIF: Level A REF: MLP10245 TOP: Lesson 1.4 Measure and Classify Angles KEY: angle measure BLM: Knowledge 3. ANS: B PTS: 1 DIF: Level A REF: XMOD0506 TOP: Lesson 1.4 Measure and Classify Angles KEY: angle name BLM: Knowledge 4. ANS: C PTS: 1 DIF: Level B REF: MIM20664 STA: MI.MIGLC.MTH.06.9-12.G1.1.1 TOP: Lesson 1.5 Describe Angle Pair Relationships KEY: angle measure supplementary angles straight angle BLM: Synthesis 5. ANS: A PTS: 1 DIF: Level A REF: MLGE0042 TOP: Lesson 1.6 Classify Polygons KEY: identify polygon BLM: Knowledge 6. ANS: A PTS: 1 DIF: Level A REF: MLGE0043 TOP: Lesson 1.6 Classify Polygons KEY: identify polygon convex BLM: Knowledge 7. ANS: D PTS: 1 DIF: Level B REF: PMG60223 TOP: Lesson 1.6 Classify Polygons KEY: identify polygon BLM: Comprehension 8. ANS: C PTS: 1 REF: 62ac50f0-4f27-11db-b4d8-0011258082f7 TOP: Lesson 1.7 Find Perimeter, Circumference, and Area KEY: perimeter of a rectangle area of a rectangle BLM: Analysis 9. ANS: D PTS: 1 DIF: Level B REF: MLC30917 TOP: Lesson 2.1 Use Inductive Reasoning KEY: scatter plot BLM: Analysis 10. ANS: A PTS: 1 DIF: Level A REF: MGEH0016 TOP: Lesson 2.2 Analyze Conditional Statements KEY: perpendicular ray BLM: Comprehension 11. ANS: D PTS: 1 DIF: Level B REF: MHGT0087 NAT: NCTM 9-12.GEO.1.a STA: MI.MIGLC.MTH.06.9-12.L3.3.3 TOP: Lesson 2.4 Use Postulates and Diagrams KEY: line point collinear BLM: Comprehension 12. ANS: D PTS: 1 DIF: Level A REF: MLGE0178 NAT: NCTM 9-12.ALG.2.b TOP: Lesson 2.5 Reason Using Properties from Algebra KEY: equality symmetric transitive reflexive BLM: Knowledge 13. ANS: B PTS: 1 DIF: Level A REF: MLGE0196 NAT: NCTM 9-12.GEO.1.a STA: MI.MIGLC.MTH.06.9-12.L3.3.3 TOP: Lesson 2.7 Prove Angle Pair Relationships KEY: line vertical angle intersecting BLM: Comprehension 1

14. ANS: D PTS: 1 DIF: Level B REF: MGEH0026 NAT: NCTM 9-12.GEO.1.a STA: MI.MIGLC.MTH.06.9-12.G1.1.2 TOP: Lesson 3.2 Use Parallel Lines and Transversals KEY: parallel transversal BLM: Analysis 15. ANS: C PTS: 1 DIF: Level B REF: MLGE0207 NAT: NCTM 9-12.GEO.1.a TOP: Lesson 3.2 Use Parallel Lines and Transversals KEY: angles parallel lines transversal BLM: Analysis 16. ANS: B PTS: 1 DIF: Level B REF: MCT90022 NAT: NCTM 9-12.GEO.1.a TOP: Lesson 3.2 Use Parallel Lines and Transversals KEY: vertical angle parallel transversal congruent corresponding BLM: Analysis 17. ANS: D PTS: 1 DIF: Level B REF: BMGM0362 STA: MI.MIGLC.MTH.06.9-12.A3.1.4 TOP: Lesson 3.4 Find and Use Slopes of Lines KEY: line slope parallel perpendicular BLM: Comprehension 18. ANS: A PTS: 1 DIF: Level B REF: MHGM0007 STA: MI.MIGLC.MTH.06.9-12.A1.2.9 MI.MIGLC.MTH.06.9-12.A3.1.4 TOP: Lesson 3.4 Find and Use Slopes of Lines KEY: line slope parallel perpendicular 19. ANS: D PTS: 1 DIF: Level B REF: MHGM0504 STA: MI.MIGLC.MTH.06.9-12.A1.2.9 MI.MIGLC.MTH.06.9-12.A3.1.4 TOP: Lesson 3.4 Find and Use Slopes of Lines KEY: slope parallel perpendicular BLM: Comprehension 20. ANS: D PTS: 1 DIF: Level B REF: MALG0666 NAT: NCTM 9-12.ALG.4.a TOP: Lesson 3.4 Find and Use Slopes of Lines KEY: interpret graph BLM: Application 21. ANS: B PTS: 1 DIF: Level B REF: BMGM0364 STA: MI.MIGLC.MTH.06.9-12.A3.1.4 TOP: Lesson 3.5 Write and Graph Equations of Lines KEY: equation slope parallel perpendicular BLM: Comprehension 22. ANS: D PM: Fixed duplicate answer error. PTS: 1 DIF: Level B REF: MC100268 TOP: Lesson 3.5 Write and Graph Equations of Lines KEY: linear equation graph change parameter BLM: Analysis 23. ANS: A PTS: 1 DIF: Level A REF: HLGM0266 NAT: NCTM 9-12.GEO.1.a STA: MI.MIGLC.MTH.06.9-12.G1.2.2 TOP: Lesson 4.1 Apply Triangle Sum Properties KEY: angle acute triangle measure BLM: Knowledge 24. ANS: B PTS: 1 DIF: Level B REF: MC100123 STA: MI.MIGLC.MTH.06.9-12.G1.2.2 TOP: Lesson 4.1 Apply Triangle Sum Properties KEY: triangle perimeter side isosceles BLM: Application 2

25. ANS: C PTS: 1 DIF: Level B REF: DJAM1027 NAT: NCTM 9-12.GEO.1.b STA: MI.MIGLC.MTH.06.9-12.G2.3.1 MI.MIGLC.MTH.06.9-12.G2.3.2 TOP: Lesson 4.2 Apply Congruence and Triangles KEY: triangles congruent BLM: Comprehension 26. ANS: A PTS: 1 DIF: Level B REF: MCT90021 STA: MI.MIGLC.MTH.06.9-12.G1.1.2 TOP: Lesson 4.2 Apply Congruence and Triangles KEY: triangle congruent BLM: Comprehension 27. ANS: C PTS: 1 DIF: Level B REF: MGCS0293 TOP: Lesson 4.3 Prove Triangles Congruent by SSS KEY: triangle congruent BLM: Comprehension 28. ANS: C PTS: 1 DIF: Level B REF: MLGE0234 STA: MI.MIGLC.MTH.06.9-12.G2.3.1 MI.MIGLC.MTH.06.9-12.G2.3.2 TOP: Lesson 4.4 Prove Triangles Congruent by SAS and HL KEY: triangle parallel lines congruence ASA SAS BLM: Comprehension 29. ANS: D PTS: 1 DIF: Level C REF: HLGM0274 NAT: NCTM 9-12.REP.2 NCTM 9-12.PRS.3 NCTM 9-12.GEO.1.a STA: MI.MIGLC.MTH.06.9-12.A1.2.1 MI.MIGLC.MTH.06.9-12.G1.2.2 TOP: Lesson 4.7 Use Isosceles and Equilateral Triangles KEY: triangle segment congruent BLM: Comprehension 30. ANS: C PTS: 1 DIF: Level C REF: HLGM0315 STA: MI.MIGLC.MTH.06.9-12.G2.3.1 MI.MIGLC.MTH.06.9-12.G2.3.2 TOP: Lesson 4.7 Use Isosceles and Equilateral Triangles KEY: triangle segment congruent BLM: Comprehension 31. ANS: B PTS: 1 DIF: Level A REF: TASH0022 STA: MI.MIGLC.MTH.06.9-12.G3.1.1 MI.MIGLC.MTH.06.9-12.G3.1.3 TOP: Lesson 4.8 Perform Congruence Transformations KEY: reflection rotation translation BLM: Knowledge 32. ANS: B PTS: 1 DIF: Level A REF: DD020284 STA: MI.MIGLC.MTH.06.9-12.G3.1.1 MI.MIGLC.MTH.06.9-12.G3.1.3 TOP: Lesson 4.8 Perform Congruence Transformations KEY: translations BLM: Knowledge 33. ANS: C PTS: 1 DIF: Level C REF: MC100132 STA: MI.MIGLC.MTH.06.9-12.G3.1.1 MI.MIGLC.MTH.06.9-12.G3.1.3 TOP: Lesson 4.8 Perform Congruence Transformations KEY: word rotation transformation BLM: Application 34. ANS: A PTS: 1 DIF: Level B REF: MHGM0083 STA: MI.MIGLC.MTH.06.9-12.G1.1.3 TOP: Lesson 5.2 Use Perpendicular Bisectors KEY: perpendicular bisector BLM: Comprehension 35. ANS: B PTS: 1 DIF: Level B REF: HLGM0344 STA: MI.MIGLC.MTH.06.9-12.G1.2.5 TOP: Lesson 5.3 Use Angle Bisectors of Triangles KEY: angle triangle perpendicular bisect BLM: Comprehension 3

36. ANS: B PTS: 1 DIF: Level B REF: MLGE0348 TOP: Lesson 5.5 Use Inequalities in a Triangle KEY: triangle inequality theorem BLM: Application 37. ANS: D PTS: 1 DIF: Level B REF: PHGM0418 TOP: Lesson 5.5 Use Inequalities in a Triangle KEY: triangle inequality BLM: Comprehension 38. ANS: B PTS: 1 DIF: Level B REF: MLGE0060 TOP: Lesson 5.6 Inequalities in Two Triangles and Indirect Proof KEY: triangle congruent Hinge Theorem BLM: Comprehension 39. ANS: C PTS: 1 DIF: Level B REF: MLGE0061 TOP: Lesson 5.6 Inequalities in Two Triangles and Indirect Proof KEY: triangle congruent Hinge Theorem BLM: Comprehension 40. ANS: D PTS: 1 DIF: Level B REF: MGEO0009 TOP: Lesson 5.6 Inequalities in Two Triangles and Indirect Proof KEY: triangle congruent Hinge Theorem BLM: Comprehension 41. ANS: C PTS: 1 DIF: Level B REF: HLGM0411 TOP: Lesson 5.6 Inequalities in Two Triangles and Indirect Proof KEY: triangle Hinge Theorem BLM: Comprehension 42. ANS: A PTS: 1 DIF: Level A REF: HLGM0410 TOP: Lesson 5.6 Inequalities in Two Triangles and Indirect Proof KEY: compare triangle measure BLM: Knowledge 43. ANS: D PTS: 1 DIF: Level B REF: HLGM0609 TOP: Lesson 6.1 Ratios, Proportions, and Geometric Mean KEY: proportion BLM: Comprehension 44. ANS: C PTS: 1 DIF: Level A REF: HLGM0611 TOP: Lesson 6.2 Use Proportions to Solve Geometry Problems KEY: solve proportion BLM: Knowledge 45. ANS: D PTS: 1 DIF: Level B REF: AXG80675 NAT: NCTM 9-12.MEA.1.a TOP: Lesson 6.2 Use Proportions to Solve Geometry Problems KEY: ratio word proportion scale BLM: Application 46. ANS: D PTS: 1 DIF: Level B REF: MLGE0169 NAT: NCTM 9-12.GEO.1.b STA: MI.MIGLC.MTH.06.9-12.G2.3.3 MI.MIGLC.MTH.06.9-12.G2.3.4 TOP: Lesson 6.4 Prove Triangles Similar by AA KEY: similar triangle BLM: Comprehension 47. ANS: A PTS: 1 DIF: Level B REF: HLGM0641 STA: MI.MIGLC.MTH.06.9-12.G2.3.3 MI.MIGLC.MTH.06.9-12.G2.3.4 TOP: Lesson 6.5 Prove Triangles Similar by SSS and SAS KEY: similar triangle rule BLM: Knowledge 48. ANS: B PTS: 1 DIF: Level A REF: HLGM0644 STA: MI.MIGLC.MTH.06.9-12.G2.3.3 MI.MIGLC.MTH.06.9-12.G2.3.4 TOP: Lesson 6.5 Prove Triangles Similar by SSS and SAS KEY: side corresponding proportional BLM: Knowledge 4

49. ANS: B PTS: 1 DIF: Level B REF: HLGM0665 TOP: Lesson 6.6 Use Proportionality Theorems KEY: proportion similar triangle BLM: Comprehension 50. ANS: D PTS: 1 DIF: Level B REF: 62ac7800-4f27-11db-b4d8-0011258082f7 TOP: Lesson 6.7 Perform Similarity Transformations KEY: dilation similar figures BLM: Comprehension 5

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