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Practice CFor use with the lesson “Identify Pairs of Lines and Angles”

Think of each segment in the diagram as part of a line. Complete the statement with parallel, skew, or perpendicular.

1. @##$ WZ and @##$ XY are ? .

W

X Y

Z

Q T

SR

2. @##$ WZ and @##$ YZ are ? .

3. @##$ RS and @##$ TZ are ? .

4. Plane WQR and plane SYT are ? .

5. Plane RQW and plane TQW are ? .

Think of each segment in the diagram as part of a line. Which line(s) or plane(s) appear to fit the description?

6. Line(s) parallel to @##$ RX

W

X Y

Z

Q T

SR

7. Line(s) perpendicular to @##$ TZ

8. Line(s) skew to @##$ XY and containing point S

9. Plane(s) perpendicular to plane STZ

10. Plane(s) parallel to plane QRS

Classify the angle pair as corresponding, alternate interior, alternate exterior, or consecutive interior angles.

11. ∠1 and ∠ 5 1 2

34 5 678

13 141516

9 101112

12. ∠ 4 and ∠ 6

13. ∠16 and ∠10

14. ∠11 and ∠16

15. ∠12 and ∠14

16. ∠ 7 and ∠13

In Exercises 17–20, use the markings in the diagram.

17. Name a pair of parallel lines. O

T

L M

N

S

P

R

V

Q 18. Name a pair of perpendicular lines.

19. Is @##$ QS i @###$ PM ? Explain.

20. Is @##$ OL ⊥ @##$ TR ? Explain.

Name ——————————————————————— Date ————————————

GeometryChapter Resource Book 3-9

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Copy and complete the statement with sometimes, always, or never.

21. If two lines are not perpendicular, then they are ? coplanar.

22. If two lines are coplanar, then they are ? skew.

23. If three lines are coplanar and never intersect, then they are ? parallel.

24. If two planes are parallel, then they ? intersect.

Copy the diagram and sketch the line.

25. Line through A and parallel to @##$ BC . A

B C

26. Line through A and perpendicular to @##$ BC .

27. Line through B and perpendicular to @##$ BC .

28. Line through C and parallel to @##$ AB .

Copy and complete the statement. List all possible correct answers.

29. ∠ 2 and ? are corresponding angles.

12 3

4

5 678

10 11129

30. ∠ 4 and ? are consecutive interior angles.

31. ∠11 and ? are alternate interior angles.

32. ∠12 and ? are alternate exterior angles.

Use the diagram of the ski lift chair to decide whether the statement is true or false.

C

DBA

33. At any position around the ski lift, the line containing the crossbar @##$ AB of each chair is parallel to the ground.

34. The line containing the back support @##$ CD and the line containing the crossbar @##$ AB are skew lines.

35. At any position around the lift, the line containing the back support @##$ CD is perpendicular to the ground.

Practice C continuedFor use with the lesson “Identify Pairs of Lines and Angles”

Name ——————————————————————— Date ————————————

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Lesson Identify Pairs of Lines and AnglesTeaching Guide

1. Check drawings; Sample answer: The distance between the two lines is always the same.

2. Check drawings; Sample answer: Only one line can be drawn through the point perpendicular to the other red segment. 3. a. Check drawings. b. Check drawings; Sample answer: The lines lie in different planes and extend in different directions.

Practice Level A

1. parallel 2. perpendicular 3. skew

4. parallel 5. perpendicular 6. @##$ DC , @##$ HG , @##$ EF

7. @##$ AB , @##$ EF , @##$ BC , @##$ FG 8. @##$ AE , @##$ EH 9. plane ABC, plane EFG, plane ADH, plane BCG 10. plane EFG 11. alternate interior 12. corresponding 13. alternate interior 14. alternate exterior

15. consecutive interior 16. alternate exterior

17. @##$ PM i @##$ OL 18. } VN ⊥ } RT 19. No; the lines intersect at R. 20. Yes; there is a right angle symbol shown. 21. sometimes 22. never

23. always 24. sometimes

25. A

B C

26. A

B C

27. A

B C

28. A

B C

29. ∠1 and ∠ 5, ∠ 2 and ∠ 6, ∠ 3 and ∠ 7, ∠ 4 and ∠ 8 30. ∠ 3 and ∠ 5, ∠ 4 and ∠ 6

31. ∠1 and ∠ 7, ∠ 2 and ∠ 8 32. ∠ 3 and ∠ 6, ∠ 4 and ∠ 5 33. true 34. false 35. true

36. false

Practice Level B

1. perpendicular 2. parallel 3. skew

4. perpendicular 5. parallel 6. @##$ FG , @##$ DC , @##$ AB

7. @##$ AE , @##$ BH , @##$ EF , @##$ HG 8. @##$ EF 9. planes EFG, ABC, ADF, and BCG 10. plane EHB

11. corresponding 12. consecutive interior

13. alternate exterior 14. alternate interior

15. corresponding 16. consecutive interior

17. @##$ PM i @##$ QS 18. @##$ VN ⊥ @##$ RT 19. No; the lines intersect at T. 20. No; there is no right angle symbol shown. 21. never 22. never

23. sometimes 24. sometimes

25. N

MP

26. N

MP

27. N

MP

28. N

MP

29–30. Check students’ drawings. 31. true

32. true 33. false 34. true

Practice Level C

1. parallel 2. perpendicular 3. skew

4. parallel 5. perpendicular 6. @###$ QW , @##$ SY , @##$ TZ

7. @##$ YZ , @##$ ST , @##$ QT , @##$ WZ 8. @##$ ST

9. plane TQW, plane SRX, plane ZWX, plane SRQ 10. plane WXY

11. corresponding 12. alternate exterior

13. alternate interior 14. consecutive interior

15. alternate exterior 16. alternate interior

17. @##$ OL i @##$ VN 18. @##$ VN ⊥ @##$ RT

19. No; the markings do not indicate that the lines are parallel 20. Yes; since @##$ OL is parallel to @##$ VN and @##$ VN is perpendicular to @##$ TR 21. sometimes

22. never 23. always 24. never

25. A

B C

26. A

B C

27. A

B C

28. A

B C

29. ∠ 6, ∠10 30. ∠ 5, ∠11 31. ∠1, ∠ 8

32. ∠ 2 33. true 34. true 35. false

Study Guide

1. skew 2. parallel 3. parallel

4. perpendicular 5. @##$ AD , @##$ EH , @##$ DC , @##$ HG

6. plane ABE 7. @##$ FG 8. @##$ AE , @##$ DH , @##$ AD , @##$ DC , @##$ AB

9. alternate interior 10. corresponding

11. alternate exterior 12. consecutive interior

Interdisciplinary Application

1. 6 2. ABCD i GHJI, ADIE i BCJF

3. @##$ EF , @##$ GH , @##$ DC , @##$ IJ 4. @##$ GI , @##$ HJ ; They intersect @##$ IJ at a 908 angle. 5. @##$ IG , @##$ CD , @##$ DI , @##$ GH , @##$ IJ , @##$ AD

6. Yes. The bat is parallel to all sides of the bat house because it hangs straight down. Yes. The bat is perpendicular to the ground for the same reason.

Answers for Chapter Parallel and Perpendicular Lines

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GeometryChapter Resource Book A33

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