Parallel Lines and Planes

1. Parthenon Athens Dallas City Hall I.M. Pei Havasu Falls I.M. Pei Parallel Lines and Planes 3.1 Written Exercises

2. 3.1 Written Exercises 1 Classify each pair of angles as either alternate interior, same-side interior, or corresponding. Alternate exterior angles Z points the way.

3. 2 Classify each pair of angles as either alternate interior, same-side interior, or corresponding. Corresponding angles Same position on ladder

4. 3 Classify each pair of angles as either alternate interior, same-side interior, or corresponding. Same-side interior angles C points the way.

5. 4 Classify each pair of angles as either alternate interior, same-side interior, or corresponding. Alternate interior angles Z points the way.

6. 5 Classify each pair of angles as either alternate interior, same-side interior, or corresponding. Corresponding angles Same position on ladder

7. 6 Classify each pair of angles as either alternate interior, same-side interior, or corresponding. Corresponding angles Same position on ladder

8. 7 Name the two lines and transversal that form each pair of angles.

9. 8 Name the two lines and transversal that form each pair of angles.

10. 9 Name the two lines and transversal that form each pair of angles. Not appropriate Because the lines Are not parallel.

11. 10 Name the two lines and transversal that form each pair of angles.

12. 11 Name the two lines and transversal that form each pair of angles.

13. Classify each pair of angles as either alternate interior, same-side interior, or corresponding. 12 Corresponding angles Same position on ladder

14. Classify each pair of angles as either alternate interior, same-side interior, or corresponding. 13 Corresponding angles Same position on ladder

15. Classify each pair of angles as either alternate interior, same-side interior, or corresponding. 14 Alternate interior angles Z points the way.

16. Classify each pair of angles as either alternate interior, same-side interior, or corresponding. 15 Same-side interior angles C points the way.

17. Classify each pair of angles as either alternate interior, same-side interior, or corresponding. 16 Same-side interior angles C points the way.

18. Classify each pair of angles as either alternate interior, same-side interior, or corresponding. 17 Corresponding angles Same position on ladder

19. Alternate exterior angles Alternate interior angles Z points the way. Corresponding angles Same position on ladder Same-side interior angles C points the way. Same-side exterior angles

20. 23 Name 5 lines that appear to be // to

21. 24 Name 3 lines that appear to be // to

22. 25 Name 4 lines that appear to be skew to

23. 26 Name 2 planes that appear to be // to

24. 26 Name 2 planes that appear to be // to

25. 27 Name 4 planes that appear to be // to

26. 27 Name 4 planes that appear to be // to

27. 27 Name 4 planes that appear to be // to

28. 28 How many pairs of parallel planes are shown?

29. 28 How many pairs of parallel planes are shown?

30. 28 How many pairs of parallel planes are shown?

31. 28 How many pairs of parallel planes are shown?

32. 29 Suppose the top and bottom of the box lie in parallel planes. Explain how Theorem 3.1 can be used to prove

33. 29 Suppose the top and bottom of the box lie in parallel planes. Explain how Theorem 3.1 can be used to prove Theorem 3.1 If 2 parallel planes are cut by a third plane, then the lines of intersection are parallel.

34. 29 Suppose the top and bottom of the box lie in parallel planes. Explain how Theorem 3.1 can be used to prove Theorem 3.1 If 2 parallel planes are cut by a third plane, then the lines of intersection are parallel. Are the lines of intersection of the transversal plane CDJI.

35. Complete each statement with always, sometimes, or never. 30 When there is a transversal of two lines, the 3 lines are __________ coplanar. always Since two points of each line are in the same plane, all the lines are in the same plane. Remember, if 2 points of a line are in the plane, then the whole line is in the plane.

36. Complete each statement with always, sometimes, or never. Three lines intersecting in one point are ___________ coplanar. 31 Yes

37. Complete each statement with always, sometimes, or never. Three lines intersecting in one point are ___________ coplanar. 31 sometimes No Yes

38. Complete each statement with always, sometimes, or never. 32 never Two lines that are not coplanar ________ intersect. Intersecting lines are always coplanar And Non-intersecting are never coplanar.

39. Complete each statement with always, sometimes, or never. 33 always Two lines parallel to a third line are ________ parallel to each other

40. Complete each statement with always, sometimes, or never. sometimes 34 Two lines skew to a third line are __________ skew to each other. No No Yes

41. Complete each statement with always, sometimes, or never. 35 Two lines perpendicular to a third line are __________ perpendicular to each other. sometimes Yes No No

42. Complete each statement with always, sometimes, or never. 36 Two planes parallel to the same line are __________ parallel to each other. sometimes Yes No

43. Complete each statement with always, sometimes, or never. 37 Two planes parallel to the same plane are __________ parallel to each other. always

44. Complete each statement with always, sometimes, or never. 38 sometimes Lines in two parallel planes are _________ parallel to each other. Yes No

45. Complete each statement with always, sometimes, or never. 39 Two lines parallel to the same plane are _________ parallel to each other. sometimes Yes No

46. C’est fini. Good day and good luck.