Name ________________________________________ Date ___________________ Class __________________

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Holt McDougal Geometry

Parallel and Perpendicular Lines Chapter Test Form C

1. Identify a pair of skew segments.

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2. Write True or False. Perpendicular lines cannot be skew lines.

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3. How many total pairs of both alternate exterior and alternate interior angles are formed by a transversal that intersects two coplanar lines at two different points?

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4. Given: ∠8 and ∠6 are corresponding angles. Identify the transversal.

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5. If parallel lines are intersected by a transversal that is not perpendicular to them, how many pairs of nonadjacent supplementary angles are formed?

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6. What one word completes the following sentence? ________ angles formed by a transversal of parallel lines are congruent and all the ________ angles are supplementary to all the obtuse angles.

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7. Find the measure of ∠QRS and state the postulate or theorem that justifies your answer.

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8. If ∠1 ≅ ∠6 and m∠1 ≠ 90�, is r || s?

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9. Which values for x and y make lines r, s, and t parallel?

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10. If two parallel lines and a transversal form angles that are all congruent, describe the relationship between the transversal and each of the parallel lines.

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Holt McDougal Geometry

Parallel and Perpendicular Lines Chapter Test Form B continued

12. Write and solve an inequality for x.

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13. Complete Step 6 by stating the theorem that proves p || q.

Given: s � p and ∠1 and ∠2 are complementary.

Prove: p || q Proof:

Statements Reasons

1. s � p and ∠1 and ∠2 are complementary.

1. Given

2. m∠1 + m∠2 = 90� 2. Def. of comp. �

3. m∠HJK = m∠1 + m∠2

3. ∠ Add. Post.

4. m∠HJK = 90� 4. Trans. Prop. of =

5. s � q 5. Def. of �

6. p || q 6. ?

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14. Complete the sentence. If the product of the slopes of two lines equals −1, then the lines are _______.

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15. Determine the slope of the line through J(−4, 3) and K(6, 4).

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16. Determine whether the line through (0, 4) and (2, 0) and the line through (−2, 3) and (−4, 2) are parallel, perpendicular, or neither.

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17. Write the equation of the line through (0, 4) and (2, 0) in slope-intercept form.

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18. Write the equation of the line through (4, 4) and (2, 2) in point-slope form.

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19. Write True or False. y = −3x + 4 and y = 3x + 4 are parallel.

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20. Determine whether the lines 3x + 2y = 6 and 4y = −6x −12 are parallel, intersect, or coincide.

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Chapter

3

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Holt McDougal Geometry

Parallel and Perpendicular Lines Chapter Test Form C continued

11. Write and solve an inequality for x.

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Use the partially completed two-column proof for Exercises 12 and 13.

Given: ⊥AD BE and ∠BCF ≅ ∠FCD.

Prove: BE CF||

Proof: Statements Reasons

1. ⊥AD BE 1. Given

2. ∠BCF ≅ ∠FCD 2. Given

3. ⊥CF AD 3. ?

4. ||BE CF 4. ?

12. State the justification for Step 3.

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13. State the justification for Step 4.

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14. If the slope of a line is 0, which type of line is it and what is true about the y-coordinates of all points on the line?

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15. If line r through (4, 4) and (6, 2) is perpendicular to line s through (x, −1) and (4, y), what are possible values for x and y?

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16. If line r through (1, 1) and (5, 7) is parallel to line s through (4, −2) and (x, y), what are possible values for x and y?

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17. Write True or False. All horizontal lines are perpendicular to all vertical lines, so the product of the slope of a horizontal line and the slope of a vertical line is −1.

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18. Write True or False. Multiplying both sides of the equation for a line by the same nonzero number will produce an equation for a line that coincides with the original line.

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19. Write the equation of the line that has y-intercept 4 and is parallel to y = −2.

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20. Write an equation in slope-intercept form for the line that passes through (6, 6) and is perpendicular to −2x + 3y = −6.

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Chapter

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Holt McDougal Geometry

Answer Key Parallel and Perpendicular Lines

Section Quiz: Lessons 3-1 Through 3-4

1. D 5. A

2. H 6. G

3. B 7. C

4. G 8. J

Section Quiz: Lessons 3-5 Through 3-6

1. B 6. G

2. H 7. A

3. D 8. F

4. J 9. A

5. C 10. H

Chapter Test Form A: Multiple Choice

1. B 11. A

2. A 12. A

3. A 13. B

4. A 14. A

5. B 15. A

6. B 16. D

7. B 17. A

8. C 18. A

9. B 19. B

10. B 20. C

Chapter Test Form B: Multiple Choice

1. C 11. B

2. J 12. H

3. B 13. A

4. G 14. H

5. A 15. B

6. G 16. F

7. A 17. D

8. H 18. J

9. A 19. A

10. F 20. J

Chapter Test Form C: Multiple Choice

1. A 11. A

2. F 12. J

3. C 13. C

4. G 14. J

5. A 15. D

6. G 16. G

7. C 17. B

8. H 18. G

9. A 19. D

10. J 20. H

Chapter Test Form A: Free Response

1. Sample answer: AB and DC

2. False

3. eight

4. alternate interior angles

5. four

6. congruent

7. 135°

8. True

9. Conv. of the Alt. Ext. s∠ Thm.

10. one

11. CA

12. x + 3 < 28; x < 25

13. perpendicular

14. rise

15. 2

16. parallel

17. True

18. y = 3x − 5

19. − = −36 ( 4)4

y x

20. parallel

Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.

Holt McDougal Geometry

Chapter Test Form B: Free Response

1. Answer: , , , orAB AE DE DH

2. False

3. four

4. corresponding angles

5. two

6. congruent

7. 80°

8. Conv. of the Alt. Ext. s∠ Thm.

9. x = 25

10. perpendicular

11. BD

12. 4x < 2x + 20; x < 10

13. 2 lines ⊥ to same line → 2 lines

14. perpendicular

15. 110

16. perpendicular

17. y = −2x + 4

18. Possible answers: y − 2 = 1(x − 2) or y − 4 = 1(x − 4)

19. False

20. parallel

Chapter Test Form C: Free Response

1. Sample answer: AB and EH

2. True

3. four

4. line s

5. eight

6. acute

7. 72°; Same-Side Interior Angles Theorem

8. no

9. x = 26.25 and y = −3.75 10. The transversal is perpendicular to both

parallel lines.

11. 4x − 3 < 2x + 11; x < 7

12. 2 intersecting lines form linear pair of ≅ s∠ → lines ⊥

13. 2 lines ⊥ to same line → 2 lines

14. horizontal line; all the same

15. Sample answer: x = 3, y = 0

16. Sample answer: x = 6, y = 1

17. False

18. True

19. y = 4

20. = − +3 152

y x

Performance Assessment

1, 3, 5.

2. = −1 45 5

y x

4. = +1 45

y x

6. There are only two different angle measures, and they represent supplementary angles. The alternate interior angles are congruent, the alternate exterior angles are congruent, the corresponding angles are congruent, and the same-side interior angles are supplementary.

Cumulative Test

1. C 20. G

2. J 21. B

3. C 22. H

4. G 23. D

5. D 24. F

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