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Name: ________________________ Class: ___________________ Date: __________ ID: A 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 ? 1 Name: ________________________ ID: A 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 and AOB. The diagram is not to scale. 6. If mDEF 127, then what are mFEG and mHEG? The diagram is not to scale. 2 Name: ________________________ ID: A 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. 3 Name: ________________________ ID: A 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. 4 Name: ________________________ ID: A 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. 5 Name: ________________________ ID: A 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. 6 Name: ________________________ ID: A 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? 7 Name: ________________________ ID: A 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? 8 Name: ________________________ ID: A 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. 9 Name: ________________________ ID: A 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. 10 Name: ________________________ ID: A 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. 11 Name: ________________________ ID: A 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. 12 Name: ________________________ ID: A 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 13 Name: ________________________ ID: A 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. 14 ID: A Geometry Unit 2 Practice Exam Answer Section SHORT ANSWER 1. ANS: P, R, T PTS: 1 DIF: L3 REF: 1-4 Measuring Angles OBJ: 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 Angles OBJ: 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: OBJ: TOP: DOK: 4. ANS: 64º 1 DIF: L3 REF: 1-4 Measuring Angles 1-4.1 Find and compare the measures of angles 1-4 Problem 3 Using Congruent Angles KEY: congruent angles DOK 2 PTS: 1 DIF: L3 REF: 1-4 Measuring Angles OBJ: 1-4.1 Find and compare the measures of angles TOP: 1-4 Problem 3 Using Congruent Angles KEY: congruent angles DOK: DOK 2 5. ANS: mBOC 32; mAOB 29 PTS: OBJ: TOP: DOK: 1 DIF: L3 REF: 1-4 Measuring Angles 1-4.1 Find and compare the measures of angles 1-4 Problem 4 Using the Angle Addition Postulate KEY: Angle Addition Postulate DOK 2 1 ID: A 6. ANS: mFEG 53, mHEG 127 PTS: OBJ: TOP: DOK: 7. ANS: 61 1 DIF: L3 REF: 1-4 Measuring Angles 1-4.1 Find and compare the measures of angles 1-4 Problem 4 Using the Angle Addition Postulate KEY: Angle Addition Postulate DOK 2 PTS: 1 DIF: L3 REF: 1-4 Measuring Angles OBJ: 1-4.1 Find and compare the measures of angles TOP: 1-4 Problem 4 Using the Angle Addition Postulate KEY: Angle Addition Postulate DOK: DOK 2 8. ANS: COB PTS: 1 DIF: L3 REF: 1-5 Exploring Angle Pairs OBJ: 1-5.1 Identify special angle pairs and use their relationships to find angle measures STA: MA.912.G.4.2 TOP: 1-5 Problem 1 Identifying Angle Pairs KEY: supplementary angles DOK: DOK 1 9. ANS: COB PTS: 1 DIF: L3 REF: 1-5 Exploring Angle Pairs OBJ: 1-5.1 Identify special angle pairs and use their relationships to find angle measures STA: MA.912.G.4.2 TOP: 1-5 Problem 1 Identifying Angle Pairs KEY: supplementary angles DOK: DOK 1 10. ANS: HGE PTS: OBJ: STA: KEY: 11. ANS: FGI 1 DIF: L3 REF: 1-5 Exploring Angle Pairs 1-5.1 Identify special angle pairs and use their relationships to find angle measures MA.912.G.4.2 TOP: 1-5 Problem 1 Identifying Angle Pairs vertical angles DOK: DOK 1 PTS: OBJ: STA: KEY: 1 DIF: L3 REF: 1-5 Exploring Angle Pairs 1-5.1 Identify special angle pairs and use their relationships to find angle measures MA.912.G.4.2 TOP: 1-5 Problem 1 Identifying Angle Pairs vertical angles DOK: DOK 1 2 ID: A 12. ANS: 180; 90 PTS: 1 DIF: L2 REF: 1-5 Exploring Angle Pairs OBJ: 1-5.1 Identify special angle pairs and use their relationships to find angle measures STA: MA.912.G.4.2 TOP: 1-5 Problem 1 Identifying Angle Pairs KEY: supplementary angles | complementary angles DOK: DOK 1 13. ANS: vertical; adjacent PTS: 1 DIF: L3 REF: 1-5 Exploring Angle Pairs OBJ: 1-5.1 Identify special angle pairs and use their relationships to find angle measures STA: MA.912.G.4.2 TOP: 1-5 Problem 1 Identifying Angle Pairs KEY: adjacent angles | vertical angles DOK: DOK 1 14. ANS: 1. AB CB 2. EC ED 3. ECD and ACB are vertical angles PTS: OBJ: STA: KEY: DOK: 15. ANS: 45° 1 DIF: L3 REF: 1-5 Exploring Angle Pairs 1-5.1 Identify special angle pairs and use their relationships to find angle measures MA.912.G.4.2 TOP: 1-5 Problem 2 Making Conclusions From a Diagram vertical angles | supplementary angles | adjacent angles | right angle | congruent segments DOK 1 PTS: 1 DIF: L2 REF: 1-5 Exploring Angle Pairs OBJ: 1-5.1 Identify special angle pairs and use their relationships to find angle measures STA: MA.912.G.4.2 TOP: 1-5 Problem 3 Finding Missing Angle Measures KEY: complementary angles DOK: DOK 1 16. ANS: DFG = 49, JKL = 41 PTS: 1 DIF: L3 REF: 1-5 Exploring Angle Pairs OBJ: 1-5.1 Identify special angle pairs and use their relationships to find angle measures STA: MA.912.G.4.2 TOP: 1-5 Problem 3 Finding Missing Angle Measures KEY: complementary angles DOK: DOK 2 17. ANS: 1 37, 2 143 PTS: OBJ: STA: KEY: 1 DIF: L3 REF: 1-5 Exploring Angle Pairs 1-5.1 Identify special angle pairs and use their relationships to find angle measures MA.912.G.4.2 TOP: 1-5 Problem 3 Finding Missing Angle Measures supplementary angles| linear pair DOK: DOK 2 3 ID: A 18. ANS: 135, 45 PTS: 1 DIF: L3 REF: 1-5 Exploring Angle Pairs OBJ: 1-5.1 Identify special angle pairs and use their relationships to find angle measures STA: MA.912.G.4.2 TOP: 1-5 Problem 3 Finding Missing Angle Measures KEY: linear pair | supplementary angles DOK: DOK 2 19. ANS: 6x – 12 PTS: 1 DIF: L3 REF: 1-5 Exploring Angle Pairs OBJ: 1-5.1 Identify special angle pairs and use their relationships to find angle measures STA: 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: OBJ: STA: TOP: KEY: 21. ANS: 64 1 DIF: L3 REF: 1-5 Exploring Angle Pairs 1-5.1 Identify special angle pairs and use their relationships to find angle measures MA.912.G.4.2 1-5 Problem 4 Using an Angle Bisector to Find Angle Measures angle bisector DOK: DOK 2 PTS: OBJ: STA: TOP: KEY: 22. ANS: 14 1 DIF: L3 REF: 1-5 Exploring Angle Pairs 1-5.1 Identify special angle pairs and use their relationships to find angle measures MA.912.G.4.2 1-5 Problem 4 Using an Angle Bisector to Find Angle Measures angle bisector DOK: DOK 2 PTS: OBJ: STA: TOP: KEY: 23. ANS: 47 1 DIF: L3 REF: 2-6 Proving Angles Congruent 2-6.1 Prove and apply theorems about angles MA.912.D.6.4| MA.912.G.8.1| MA.912.G.8.5 2-6 Problem 1 Using the Vertical Angles Theorem vertical angles | Vertical Angles Theorem DOK: DOK 2 PTS: OBJ: STA: TOP: KEY: 1 DIF: L2 REF: 2-6 Proving Angles Congruent 2-6.1 Prove and apply theorems about angles MA.912.D.6.4| MA.912.G.8.1| MA.912.G.8.5 2-6 Problem 1 Using the Vertical Angles Theorem vertical angles | Vertical Angles Theorem DOK: DOK 2 4 ID: A 24. ANS: 120 PTS: 1 DIF: L2 REF: 2-6 Proving Angles Congruent OBJ: 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 Congruent OBJ: 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 question DOK: 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.7.2 TOP: 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.7.2 TOP: 3-1 Problem 1 Identifying Nonintersecting Lines and Planes KEY: parallel | planes DOK: DOK 2 28. ANS: 3 and 4 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 Pair KEY: transversal | angle pair DOK: DOK 1 29. ANS: angles 2 & 4, 3 & 5, and 1 & 7 PTS: OBJ: STA: KEY: 1 DIF: L3 REF: 3-1 Lines and Angles 3-1.2 Identify angles formed by two lines and a transversal MA.912.G.7.2 TOP: 3-1 Problem 2 Identifying an Angle Pair angle pair | transversal DOK: DOK 1 5 ID: A 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 Pair KEY: angle pair | transversal DOK: DOK 1 31. ANS: alternate interior angles PTS: OBJ: STA: KEY: 32. ANS: 246 1 DIF: L2 REF: 3-1 Lines and Angles 3-1.2 Identify angles formed by two lines and a transversal MA.912.G.7.2 TOP: 3-1 Problem 3 Classifying an Angle Pair parallel lines | transversal | angle DOK: DOK 1 PTS: OBJ: STA: KEY: 33. ANS: 132 1 DIF: L3 REF: 3-2 Properties of Parallel Lines 3-2.2 Use properties of parallel lines to find angle measures MA.912.G.1.3 TOP: 3-2 Problem 3 Finding Measures of Angles parallel lines | transversal DOK: DOK 2 PTS: OBJ: STA: KEY: 34. ANS: 73 1 DIF: L3 REF: 3-2 Properties of Parallel Lines 3-2.2 Use properties of parallel lines to find angle measures MA.912.G.1.3 TOP: 3-2 Problem 1 Identifying Congruent Angles parallel lines | alternate interior angles DOK: DOK 2 PTS: OBJ: STA: KEY: 35. ANS: 31º 1 DIF: L4 REF: 3-2 Properties of Parallel Lines 3-2.2 Use properties of parallel lines to find angle measures MA.912.G.1.3 TOP: 3-2 Problem 3 Finding Measures of Angles angle | parallel lines | transversal DOK: DOK 2 PTS: OBJ: STA: KEY: 1 DIF: L3 REF: 3-2 Properties of Parallel Lines 3-2.2 Use properties of parallel lines to find angle measures MA.912.G.1.3 TOP: 3-2 Problem 3 Finding Measures of Angles angle | parallel lines | transversal DOK: DOK 2 6 ID: A 36. ANS: 64º PTS: OBJ: STA: KEY: 37. ANS: 16 1 DIF: L3 REF: 3-2 Properties of Parallel Lines 3-2.2 Use properties of parallel lines to find angle measures MA.912.G.1.3 TOP: 3-2 Problem 3 Finding Measures of Angles angle | parallel lines | transversal DOK: DOK 2 PTS: OBJ: STA: KEY: 38. ANS: 18 1 DIF: L4 REF: 3-2 Properties of Parallel Lines 3-2.2 Use properties of parallel lines to find angle measures MA.912.G.1.3 TOP: 3-2 Problem 4 Using Algebra to Find an Angle Measure corresponding angles | parallel lines | angle pairs DOK: DOK 2 PTS: 1 DIF: L3 REF: 3-2 Properties of Parallel Lines OBJ: 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 KEY: 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 Lines OBJ: 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: OBJ: TOP: DOK: 41. ANS: 61 1 DIF: L2 REF: 3-3 Proving Lines Parallel 3-3.1 Determine whether two lines are parallel STA: MA.912.G.1.3| MA.912.G.8.5 3-3 Problem 1 Identifying Parallel Lines KEY: parallel lines | reasoning DOK 2 PTS: OBJ: TOP: DOK: 1 DIF: L4 REF: 3-3 Proving Lines Parallel 3-3.1 Determine whether two lines are parallel STA: MA.912.G.1.3| MA.912.G.8.5 3-3 Problem 4 Using Algebra KEY: parallel lines | angle pairs DOK 2 7 ID: A 42. ANS: 32 PTS: OBJ: TOP: DOK: 43. ANS: 37 1 DIF: L4 REF: 3-3 Proving Lines Parallel 3-3.1 Determine whether two lines are parallel STA: MA.912.G.1.3| MA.912.G.8.5 3-3 Problem 4 Using Algebra KEY: parallel lines | transversal DOK 2 PTS: 1 DIF: L3 REF: 3-3 Proving Lines Parallel OBJ: 3-3.1 Determine whether two lines are parallel STA: MA.912.G.1.3| MA.912.G.8.5 TOP: 3-3 Problem 4 Using Algebra KEY: parallel lines | transversal DOK: DOK 2 44. ANS: The two tracks are parallel by the Perpendicular Transversal Theorem. PTS: 1 DIF: L2 REF: 3-4 Parallel and Perpendicular Lines OBJ: 3-4.1 Relate parallel and perpendicular lines STA: MA.912.G.1.3 TOP: 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: OBJ: TOP: KEY: DOK: 46. ANS: 82 1 DIF: L3 REF: 3-4 Parallel and Perpendicular Lines 3-4.1 Relate parallel and perpendicular lines STA: MA.912.G.1.3 3-4 Problem 1 Solving a Problem with Parallel Lines parallel | perpendicular | transversal | word problem | reasoning DOK 2 PTS: 1 DIF: L2 REF: 3-5 Parallel Lines and Triangles OBJ: 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 triangle DOK: DOK 2 47. ANS: x 82, y 70, z 98 PTS: OBJ: STA: TOP: DOK: 1 DIF: L3 REF: 3-5 Parallel Lines and Triangles 3-5.2 Find measures of angles of triangles MA.912.G.2.2| MA.912.G.4.1| MA.912.G.8.5 3-5 Problem 1 Using the Triangle Angle-Sum Theorem KEY: triangle | sum of angles of a triangle DOK 2 8 ID: A 48. ANS: 47 PTS: OBJ: STA: TOP: KEY: 49. ANS: 73 1 DIF: L2 REF: 3-5 Parallel Lines and Triangles 3-5.2 Find measures of angles of triangles MA.912.G.2.2| MA.912.G.4.1| MA.912.G.8.5 3-5 Problem 2 Using the Triangle Exterior Angle Theorem triangle | sum of angles of a triangle DOK: DOK 2 PTS: OBJ: STA: TOP: KEY: 50. ANS: 18 1 DIF: L4 REF: 3-5 Parallel Lines and Triangles 3-5.2 Find measures of angles of triangles MA.912.G.2.2| MA.912.G.4.1| MA.912.G.8.5 3-5 Problem 2 Using the Triangle Exterior Angle Theorem exterior angle DOK: DOK 2 PTS: OBJ: STA: TOP: KEY: 51. ANS: 40 1 DIF: L3 REF: 3-5 Parallel Lines and Triangles 3-5.2 Find measures of angles of triangles MA.912.G.2.2| MA.912.G.4.1| MA.912.G.8.5 3-5 Problem 2 Using the Triangle Exterior Angle Theorem triangle | sum of angles of a triangle | vertical angles DOK: DOK 2 PTS: OBJ: STA: TOP: DOK: 52. ANS: 103 1 DIF: L3 REF: 3-5 Parallel Lines and Triangles 3-5.2 Find measures of angles of triangles MA.912.G.2.2| MA.912.G.4.1| MA.912.G.8.5 3-5 Problem 3 Applying the Triangle Theorems KEY: triangle | angle | word problem DOK 2 PTS: OBJ: STA: TOP: KEY: 1 DIF: L3 REF: 3-5 Parallel Lines and Triangles 3-5.2 Find measures of angles of triangles MA.912.G.2.2| MA.912.G.4.1| MA.912.G.8.5 3-5 Problem 3 Applying the Triangle Theorems triangle | sum of angles of a triangle | word problem DOK: DOK 2 9 ID: A 53. ANS: 66 PTS: OBJ: STA: TOP: KEY: DOK: 1 DIF: L3 REF: 3-5 Parallel Lines and Triangles 3-5.2 Find measures of angles of triangles MA.912.G.2.2| MA.912.G.4.1| MA.912.G.8.5 3-5 Problem 3 Applying the Triangle Theorems triangle | sum of angles of a triangle | word problem | exterior angle theorem DOK 2 10