Name: ________________________ Class: ___________________ Date: __________ ID: A

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Geometry Unit 2 Practice Exam

Short Answer

1. Judging by appearance, name an acute angle, an obtuse angle, and a right angle.

2. What are the measures of FBD and ABC? Classify each angle as acute, right, obtuse, or straight.

3. Complete the statement.

DEF ?

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4. Complete the statement.The drawing is not to scale.

If mDFG 64º, then mDFE ? .

5. If mAOC 61, mBOC 2x 10, and mAOB 4x 15, find the degree measure of BOC andAOB. The diagram is not to scale.

6. If mDEF 127, then what are mFEG and mHEG? The diagram is not to scale.

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7. If mEOF 31 and mFOG 30, then what is the measure of EOG? The diagram is not to scale.

8. Name an angle supplementary to BOE.

9. Name an angle complementary to DOC.

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10. Name an angle vertical to FGI.

11. Name an angle adjacent to DGF.

12. Supplementary angles are two angles whose measures have a sum of ____.Complementary angles are two angles whose measures have a sum of ____.

13. 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.

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14. What can you conclude from the information in the diagram?

15. The complement of an angle is 45°. What is the measure of the angle?

16. DFG and JKL are complementary angles. mDFG = x 2, and mJKL = x 6. Find the measure of each angle.

17. 1 and 2 are a linear pair. m1 x 32, and m2 x 74. Find the measure of each angle.

18. Angle A and angle B are a linear pair. If mA 3mB, find mA and mB.

19. SQ

bisects RST , and mRSQ 3x 6. Write an expression for RST . The diagram is not to scale.

20. MO

bisects LMN, mLMO 8x 24, and mNMO 3x 31. Solve for x and find mLMN. The diagram is not to scale.

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21. MO

bisects LMN , mLMN 5x 22, mLMO x 34. Find mNMO. The diagram is not to scale.

22. What is the value of x?

23. What is the value of x?

24. m1 120. Find m3.

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25. Find the values of x and y.

26. What four segments are parallel to plane KLMJ?

27. What four segments are perpendicular to plane JKPN?

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Use the diagram to find the following.

28. Identify a pair of same-side interior angles.

29. What are three pairs of corresponding angles?

30. What is the relationship between 1 and 8?

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This diagram of airport runway intersections shows two parallel runways. A taxiway crosses both runways.

31. How are 6 and 3 related?

32. If 8 measures 123, what is the sum of the measures of 1 and 4?

33. Line r is parallel to line t. Find m5. The diagram is not to scale.

34. Find mQ. The diagram is not to scale.

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35. Find mG. The diagram is not to scale.

36. Find mP. The diagram is not to scale.

37. Find the value of x. The diagram is not to scale.

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38. Find the value of x. The diagram is not to scale.

39. Find the values of x and y. The diagram is not to scale.

40. Which lines are parallel if m3 m6? Justify your answer.

41. Find the value of x for which p is parallel to q, if m1 2x and m3 122.The diagram is not to scale.

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42. Find the value of x for which l is parallel to m. The diagram is not to scale.

43. Find the value of x for which l is parallel to m. The diagram is not to scale.

44. Each tie on the railroad tracks is perpendicular to both of the tracks. What is the relationship between the two tracks? Justify your answer.

45. Each sheet of metal on a roof is parallel to the rest of the sheets of metal. If the first sheet of metal is perpendicular to the top line of the roof, what can you conclude about the rest of sheets of metal? Justify your answer.

Name: ________________________ ID: A

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46. Find the value of k. The diagram is not to scale.

47. Find the values of x, y, and z. The diagram is not to scale.

48. Find the value of x. The diagram is not to scale.

49. Find the value of x. The diagram is not to scale.

Given: SRT STR, mSRT 34, mSTU 2x

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50. Find the value of x. The diagram is not to scale.

51. A triangular playground has angles with measures in the ratio 4 : 9 : 5. What is the measure of the smallest angle?

52. The folding chair has different settings that change the angles formed by its parts. Suppose m2 is 25 and m3 is 78. Find m1. The diagram is not to scale.

53. A star patterned quilt has a star with the angles shown. What is the value of x? The diagram is not to scale.

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Geometry Unit 2 Practice ExamAnswer Section

SHORT ANSWER

1. ANS: P, R, T

PTS: 1 DIF: L3 REF: 1-4 Measuring AnglesOBJ: 1-4.1 Find and compare the measures of angles TOP: 1-4 Problem 2 Measuring and Classifying Angles KEY: acute angle | right angle | obtuse angle DOK: DOK 2

2. ANS: mFBD 74; FBD is acute.mABC 180; ABC is straight.

PTS: 1 DIF: L3 REF: 1-4 Measuring AnglesOBJ: 1-4.1 Find and compare the measures of angles TOP: 1-4 Problem 2 Measuring and Classifying Angles KEY: acute angle | right angle | obtuse angle DOK: DOK 2

3. ANS: DGF

PTS: 1 DIF: L3 REF: 1-4 Measuring AnglesOBJ: 1-4.1 Find and compare the measures of angles TOP: 1-4 Problem 3 Using Congruent Angles KEY: congruent anglesDOK: DOK 2

4. ANS: 64º

PTS: 1 DIF: L3 REF: 1-4 Measuring AnglesOBJ: 1-4.1 Find and compare the measures of angles TOP: 1-4 Problem 3 Using Congruent Angles KEY: congruent anglesDOK: DOK 2

5. ANS: mBOC 32; mAOB 29

PTS: 1 DIF: L3 REF: 1-4 Measuring AnglesOBJ: 1-4.1 Find and compare the measures of angles TOP: 1-4 Problem 4 Using the Angle Addition Postulate KEY: Angle Addition PostulateDOK: DOK 2

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6. ANS: mFEG 53, mHEG 127

PTS: 1 DIF: L3 REF: 1-4 Measuring AnglesOBJ: 1-4.1 Find and compare the measures of angles TOP: 1-4 Problem 4 Using the Angle Addition Postulate KEY: Angle Addition PostulateDOK: DOK 2

7. ANS: 61

PTS: 1 DIF: L3 REF: 1-4 Measuring AnglesOBJ: 1-4.1 Find and compare the measures of angles TOP: 1-4 Problem 4 Using the Angle Addition Postulate KEY: Angle Addition PostulateDOK: DOK 2

8. ANS: COB

PTS: 1 DIF: L3 REF: 1-5 Exploring Angle PairsOBJ: 1-5.1 Identify special angle pairs and use their relationships to find angle measuresSTA: MA.912.G.4.2 TOP: 1-5 Problem 1 Identifying Angle PairsKEY: supplementary angles DOK: DOK 1

9. ANS: COB

PTS: 1 DIF: L3 REF: 1-5 Exploring Angle PairsOBJ: 1-5.1 Identify special angle pairs and use their relationships to find angle measuresSTA: MA.912.G.4.2 TOP: 1-5 Problem 1 Identifying Angle PairsKEY: supplementary angles DOK: DOK 1

10. ANS: HGE

PTS: 1 DIF: L3 REF: 1-5 Exploring Angle PairsOBJ: 1-5.1 Identify special angle pairs and use their relationships to find angle measuresSTA: MA.912.G.4.2 TOP: 1-5 Problem 1 Identifying Angle PairsKEY: vertical angles DOK: DOK 1

11. ANS: FGI

PTS: 1 DIF: L3 REF: 1-5 Exploring Angle PairsOBJ: 1-5.1 Identify special angle pairs and use their relationships to find angle measuresSTA: MA.912.G.4.2 TOP: 1-5 Problem 1 Identifying Angle PairsKEY: vertical angles DOK: DOK 1

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12. ANS: 180; 90

PTS: 1 DIF: L2 REF: 1-5 Exploring Angle PairsOBJ: 1-5.1 Identify special angle pairs and use their relationships to find angle measuresSTA: MA.912.G.4.2 TOP: 1-5 Problem 1 Identifying Angle PairsKEY: supplementary angles | complementary angles DOK: DOK 1

13. ANS: vertical; adjacent

PTS: 1 DIF: L3 REF: 1-5 Exploring Angle PairsOBJ: 1-5.1 Identify special angle pairs and use their relationships to find angle measuresSTA: MA.912.G.4.2 TOP: 1-5 Problem 1 Identifying Angle PairsKEY: adjacent angles | vertical angles DOK: DOK 1

14. ANS:

1. AB CB

2. EC ED3. ECD and ACB are vertical angles

PTS: 1 DIF: L3 REF: 1-5 Exploring Angle PairsOBJ: 1-5.1 Identify special angle pairs and use their relationships to find angle measuresSTA: MA.912.G.4.2 TOP: 1-5 Problem 2 Making Conclusions From a DiagramKEY: vertical angles | supplementary angles | adjacent angles | right angle | congruent segmentsDOK: DOK 1

15. ANS: 45°

PTS: 1 DIF: L2 REF: 1-5 Exploring Angle PairsOBJ: 1-5.1 Identify special angle pairs and use their relationships to find angle measuresSTA: MA.912.G.4.2 TOP: 1-5 Problem 3 Finding Missing Angle MeasuresKEY: complementary angles DOK: DOK 1

16. ANS: DFG = 49, JKL = 41

PTS: 1 DIF: L3 REF: 1-5 Exploring Angle PairsOBJ: 1-5.1 Identify special angle pairs and use their relationships to find angle measuresSTA: MA.912.G.4.2 TOP: 1-5 Problem 3 Finding Missing Angle MeasuresKEY: complementary angles DOK: DOK 2

17. ANS: 1 37, 2 143

PTS: 1 DIF: L3 REF: 1-5 Exploring Angle PairsOBJ: 1-5.1 Identify special angle pairs and use their relationships to find angle measuresSTA: MA.912.G.4.2 TOP: 1-5 Problem 3 Finding Missing Angle MeasuresKEY: supplementary angles| linear pair DOK: DOK 2

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18. ANS: 135, 45

PTS: 1 DIF: L3 REF: 1-5 Exploring Angle PairsOBJ: 1-5.1 Identify special angle pairs and use their relationships to find angle measuresSTA: MA.912.G.4.2 TOP: 1-5 Problem 3 Finding Missing Angle MeasuresKEY: linear pair | supplementary angles DOK: DOK 2

19. ANS: 6x – 12

PTS: 1 DIF: L3 REF: 1-5 Exploring Angle PairsOBJ: 1-5.1 Identify special angle pairs and use their relationships to find angle measuresSTA: MA.912.G.4.2 TOP: 1-5 Problem 4 Using an Angle Bisector to Find Angle Measures KEY: angle bisector DOK: DOK 2

20. ANS: x = 11, mLMN 128

PTS: 1 DIF: L3 REF: 1-5 Exploring Angle PairsOBJ: 1-5.1 Identify special angle pairs and use their relationships to find angle measuresSTA: MA.912.G.4.2 TOP: 1-5 Problem 4 Using an Angle Bisector to Find Angle Measures KEY: angle bisector DOK: DOK 2

21. ANS: 64

PTS: 1 DIF: L3 REF: 1-5 Exploring Angle PairsOBJ: 1-5.1 Identify special angle pairs and use their relationships to find angle measuresSTA: MA.912.G.4.2 TOP: 1-5 Problem 4 Using an Angle Bisector to Find Angle Measures KEY: angle bisector DOK: DOK 2

22. ANS: 14

PTS: 1 DIF: L3 REF: 2-6 Proving Angles CongruentOBJ: 2-6.1 Prove and apply theorems about angles STA: MA.912.D.6.4| MA.912.G.8.1| MA.912.G.8.5 TOP: 2-6 Problem 1 Using the Vertical Angles Theorem KEY: vertical angles | Vertical Angles Theorem DOK: DOK 2

23. ANS: 47

PTS: 1 DIF: L2 REF: 2-6 Proving Angles CongruentOBJ: 2-6.1 Prove and apply theorems about angles STA: MA.912.D.6.4| MA.912.G.8.1| MA.912.G.8.5 TOP: 2-6 Problem 1 Using the Vertical Angles Theorem KEY: vertical angles | Vertical Angles Theorem DOK: DOK 2

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24. ANS: 120

PTS: 1 DIF: L2 REF: 2-6 Proving Angles CongruentOBJ: 2-6.1 Prove and apply theorems about angles STA: MA.912.D.6.4| MA.912.G.8.1| MA.912.G.8.5 TOP: 2-6 Problem 1 Using the Vertical Angles Theorem KEY: Vertical Angles Theorem | vertical angles DOK: DOK 2

25. ANS: x = 47, y = 12

PTS: 1 DIF: L4 REF: 2-6 Proving Angles CongruentOBJ: 2-6.1 Prove and apply theorems about angles STA: MA.912.D.6.4| MA.912.G.8.1| MA.912.G.8.5 TOP: 2-6 Problem 1 Using the Vertical Angles Theorem KEY: Vertical Angles Theorem | vertical angles | supplementary angles | multi-part questionDOK: DOK 2

26. ANS: segments PQ, QR, NR, and NP

PTS: 1 DIF: L3 REF: 3-1 Lines and Angles OBJ: 3-1.1 Identify relationships between figures in space STA: MA.912.G.7.2TOP: 3-1 Problem 1 Identifying Nonintersecting Lines and Planes KEY: parallel | planes DOK: DOK 2

27. ANS: segments JM, KL, PQ, and NR

PTS: 1 DIF: L3 REF: 3-1 Lines and Angles OBJ: 3-1.1 Identify relationships between figures in space STA: MA.912.G.7.2TOP: 3-1 Problem 1 Identifying Nonintersecting Lines and Planes KEY: parallel | planes DOK: DOK 2

28. ANS: 3 and4

PTS: 1 DIF: L3 REF: 3-1 Lines and Angles OBJ: 3-1.2 Identify angles formed by two lines and a transversal STA: MA.912.G.7.2 TOP: 3-1 Problem 2 Identifying an Angle PairKEY: transversal | angle pair DOK: DOK 1

29. ANS: angles 2 & 4, 3 & 5, and 1 & 7

PTS: 1 DIF: L3 REF: 3-1 Lines and Angles OBJ: 3-1.2 Identify angles formed by two lines and a transversal STA: MA.912.G.7.2 TOP: 3-1 Problem 2 Identifying an Angle PairKEY: angle pair | transversal DOK: DOK 1

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30. ANS: alternate exterior angles

PTS: 1 DIF: L3 REF: 3-1 Lines and Angles OBJ: 3-1.2 Identify angles formed by two lines and a transversal STA: MA.912.G.7.2 TOP: 3-1 Problem 3 Classifying an Angle PairKEY: angle pair | transversal DOK: DOK 1

31. ANS: alternate interior angles

PTS: 1 DIF: L2 REF: 3-1 Lines and Angles OBJ: 3-1.2 Identify angles formed by two lines and a transversal STA: MA.912.G.7.2 TOP: 3-1 Problem 3 Classifying an Angle PairKEY: parallel lines | transversal | angle DOK: DOK 1

32. ANS: 246

PTS: 1 DIF: L3 REF: 3-2 Properties of Parallel LinesOBJ: 3-2.2 Use properties of parallel lines to find angle measures STA: MA.912.G.1.3 TOP: 3-2 Problem 3 Finding Measures of AnglesKEY: parallel lines | transversal DOK: DOK 2

33. ANS: 132

PTS: 1 DIF: L3 REF: 3-2 Properties of Parallel LinesOBJ: 3-2.2 Use properties of parallel lines to find angle measures STA: MA.912.G.1.3 TOP: 3-2 Problem 1 Identifying Congruent AnglesKEY: parallel lines | alternate interior angles DOK: DOK 2

34. ANS: 73

PTS: 1 DIF: L4 REF: 3-2 Properties of Parallel LinesOBJ: 3-2.2 Use properties of parallel lines to find angle measures STA: MA.912.G.1.3 TOP: 3-2 Problem 3 Finding Measures of AnglesKEY: angle | parallel lines | transversal DOK: DOK 2

35. ANS: 31º

PTS: 1 DIF: L3 REF: 3-2 Properties of Parallel LinesOBJ: 3-2.2 Use properties of parallel lines to find angle measures STA: MA.912.G.1.3 TOP: 3-2 Problem 3 Finding Measures of AnglesKEY: angle | parallel lines | transversal DOK: DOK 2

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36. ANS: 64º

PTS: 1 DIF: L3 REF: 3-2 Properties of Parallel LinesOBJ: 3-2.2 Use properties of parallel lines to find angle measures STA: MA.912.G.1.3 TOP: 3-2 Problem 3 Finding Measures of AnglesKEY: angle | parallel lines | transversal DOK: DOK 2

37. ANS: 16

PTS: 1 DIF: L4 REF: 3-2 Properties of Parallel LinesOBJ: 3-2.2 Use properties of parallel lines to find angle measures STA: MA.912.G.1.3 TOP: 3-2 Problem 4 Using Algebra to Find an Angle MeasureKEY: corresponding angles | parallel lines | angle pairs DOK: DOK 2

38. ANS: 18

PTS: 1 DIF: L3 REF: 3-2 Properties of Parallel LinesOBJ: 3-2.2 Use properties of parallel lines to find angle measures STA: MA.912.G.1.3 TOP: 3-2 Problem 4 Using Algebra to Find an Angle MeasureKEY: corresponding angles | parallel lines | angle pairs DOK: DOK 2

39. ANS: x = 82, y = 48

PTS: 1 DIF: L4 REF: 3-2 Properties of Parallel LinesOBJ: 3-2.2 Use properties of parallel lines to find angle measures STA: MA.912.G.1.3 TOP: 3-2 Problem 4 Using Algebra to Find an Angle Measure | 3-1 Problem 1 Identifying Nonintersecting Lines and Planes KEY: corresponding angles | parallel lines DOK: DOK 2

40. ANS: r s, by the Converse of the Alternate Interior Angles Theorem

PTS: 1 DIF: L2 REF: 3-3 Proving Lines ParallelOBJ: 3-3.1 Determine whether two lines are parallel STA: MA.912.G.1.3| MA.912.G.8.5TOP: 3-3 Problem 1 Identifying Parallel Lines KEY: parallel lines | reasoningDOK: DOK 2

41. ANS: 61

PTS: 1 DIF: L4 REF: 3-3 Proving Lines ParallelOBJ: 3-3.1 Determine whether two lines are parallel STA: MA.912.G.1.3| MA.912.G.8.5TOP: 3-3 Problem 4 Using Algebra KEY: parallel lines | angle pairsDOK: DOK 2

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42. ANS: 32

PTS: 1 DIF: L4 REF: 3-3 Proving Lines ParallelOBJ: 3-3.1 Determine whether two lines are parallel STA: MA.912.G.1.3| MA.912.G.8.5TOP: 3-3 Problem 4 Using Algebra KEY: parallel lines | transversalDOK: DOK 2

43. ANS: 37

PTS: 1 DIF: L3 REF: 3-3 Proving Lines ParallelOBJ: 3-3.1 Determine whether two lines are parallel STA: MA.912.G.1.3| MA.912.G.8.5TOP: 3-3 Problem 4 Using Algebra KEY: parallel lines | transversalDOK: DOK 2

44. ANS: The two tracks are parallel by the Perpendicular Transversal Theorem.

PTS: 1 DIF: L2 REF: 3-4 Parallel and Perpendicular LinesOBJ: 3-4.1 Relate parallel and perpendicular lines STA: MA.912.G.1.3TOP: 3-4 Problem 1 Solving a Problem with Parallel Lines KEY: parallel | perpendicular | transversal | word problem | reasoning DOK: DOK 2

45. ANS: The sheets of metal are all perpendicular to the top line of the roof by the Perpendicular Transversal Theorem.

PTS: 1 DIF: L3 REF: 3-4 Parallel and Perpendicular LinesOBJ: 3-4.1 Relate parallel and perpendicular lines STA: MA.912.G.1.3TOP: 3-4 Problem 1 Solving a Problem with Parallel Lines KEY: parallel | perpendicular | transversal | word problem | reasoning DOK: DOK 2

46. ANS: 82

PTS: 1 DIF: L2 REF: 3-5 Parallel Lines and TrianglesOBJ: 3-5.2 Find measures of angles of triangles STA: MA.912.G.2.2| MA.912.G.4.1| MA.912.G.8.5 TOP: 3-5 Problem 1 Using the Triangle Angle-Sum Theorem KEY: triangle | sum of angles of a triangleDOK: DOK 2

47. ANS: x 82, y 70, z 98

PTS: 1 DIF: L3 REF: 3-5 Parallel Lines and TrianglesOBJ: 3-5.2 Find measures of angles of triangles STA: MA.912.G.2.2| MA.912.G.4.1| MA.912.G.8.5 TOP: 3-5 Problem 1 Using the Triangle Angle-Sum Theorem KEY: triangle | sum of angles of a triangleDOK: DOK 2

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48. ANS: 47

PTS: 1 DIF: L2 REF: 3-5 Parallel Lines and TrianglesOBJ: 3-5.2 Find measures of angles of triangles STA: MA.912.G.2.2| MA.912.G.4.1| MA.912.G.8.5 TOP: 3-5 Problem 2 Using the Triangle Exterior Angle Theorem KEY: triangle | sum of angles of a triangle DOK: DOK 2

49. ANS: 73

PTS: 1 DIF: L4 REF: 3-5 Parallel Lines and TrianglesOBJ: 3-5.2 Find measures of angles of triangles STA: MA.912.G.2.2| MA.912.G.4.1| MA.912.G.8.5 TOP: 3-5 Problem 2 Using the Triangle Exterior Angle Theorem KEY: exterior angle DOK: DOK 2

50. ANS: 18

PTS: 1 DIF: L3 REF: 3-5 Parallel Lines and TrianglesOBJ: 3-5.2 Find measures of angles of triangles STA: MA.912.G.2.2| MA.912.G.4.1| MA.912.G.8.5 TOP: 3-5 Problem 2 Using the Triangle Exterior Angle Theorem KEY: triangle | sum of angles of a triangle | vertical angles DOK: DOK 2

51. ANS: 40

PTS: 1 DIF: L3 REF: 3-5 Parallel Lines and TrianglesOBJ: 3-5.2 Find measures of angles of triangles STA: MA.912.G.2.2| MA.912.G.4.1| MA.912.G.8.5 TOP: 3-5 Problem 3 Applying the Triangle Theorems KEY: triangle | angle | word problemDOK: DOK 2

52. ANS: 103

PTS: 1 DIF: L3 REF: 3-5 Parallel Lines and TrianglesOBJ: 3-5.2 Find measures of angles of triangles STA: MA.912.G.2.2| MA.912.G.4.1| MA.912.G.8.5 TOP: 3-5 Problem 3 Applying the Triangle Theorems KEY: triangle | sum of angles of a triangle | word problem DOK: DOK 2

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53. ANS: 66

PTS: 1 DIF: L3 REF: 3-5 Parallel Lines and TrianglesOBJ: 3-5.2 Find measures of angles of triangles STA: MA.912.G.2.2| MA.912.G.4.1| MA.912.G.8.5 TOP: 3-5 Problem 3 Applying the Triangle Theorems KEY: triangle | sum of angles of a triangle | word problem | exterior angle theoremDOK: DOK 2