1. Parallel Lines and Planes Dallas City Hall I.M. Pei Parthenon Athens Havasu Falls I.M. Pei Lesson 3.1 When Lines & Planes Are //

2. Two Types of Lines Non-intersecting Intersecting

3. Types of Lines Lines either intersect or don’t. Intersecting LinesNon-intersecting 1] Perpendicular 2] non-perpendicular 4] Non-coplanar or skew 3] Coplanar or parallel //

4. Intersecting Lines 1] Perpendicular 2] non-perpendicular Non-perpendicular Perpendicular

5. Non-intersecting Lines 1] Coplanar = parallel // 2] Non-coplanar = skew

6. Identifying Types of Lines Now what about …. Note that each yellow plane is a rectangle. Parallel Non-intersecting and coplanar

7. Now what about …. Intersecting and perpendicular

8. Now what about …. Intersecting and perpendicular

9. Now what about …. Intersecting and perpendicular

10. Now what about …. Intersecting and perpendicular

11. Now what about …. Parallel Non-intersecting and coplanar

12. Now what about …. Parallel Non-intersecting and coplanar

13. Now what about …. Parallel Non-intersecting and coplanar

14. Now what about …. Skew Non-intersecting and non-coplanar

15. Now what about …. Skew Non-intersecting and non-coplanar

16. Now what about ….

17. Intersecting and non-perpendicular

18. Intersecting and perpendicular

19. Parallel Lines Coplanar and non-intersecting L1L1 L2L2

20. Parallel Lines Transversal Line L1L1 L2L2

21. Parallel Lines L1L1 L2L2 T Interior Space: Tunnel Space

22. Parallel Lines L1L1 L2L2 T Interior Space: Tunnel Space

23. Parallel Lines L1L1 L2L2 T Interior Space: Tunnel Space Exterior Space

24. Parallel Lines L1L1 L2L2 T AB C D E F G H Which angles are interior angles?

25. Parallel Lines L1L1 L2L2 T AB C D E F G H Which angles are interior angles?

26. Parallel Lines L1L1 L2L2 T AB C D E F G H Which angles are exterior angles?

27. Parallel Lines L1L1 L2L2 T AB C D E F G H Which angles are exterior angles?

28. Parallel Lines L1L1 L2L2 T AB C D E F G H Which angles are same-side angles?

29. Parallel Lines L1L1 L2L2 T AB C D E F G H Which angles are same-side angles?

30. Parallel Lines L1L1 L2L2 T AB C D E F G H Corresponding Angles Same step on the ladder

31. Parallel Lines L1L1 L2L2 T AB C D E F G H Corresponding Angles Same step on the ladder

32. Parallel Lines L1L1 L2L2 T AB C D E F G H Corresponding Angles Same step on the ladder

33. Parallel Lines L1L1 L2L2 T AB C D E F G H Corresponding Angles Same step on the ladder

34. Parallel Lines L1L1 L2L2 T AB C D E F G H Alternate Interior Angles ? Z is the key

35. Parallel Lines L1L1 L2L2 T AB C D E F G H Alternate Interior Angles ? Dyslexic Z

36. Alternate Interior Angles Are Congruent

37. Parallel Lines L1L1 L2L2 T AB C D E F G H Same-side Interior Angles ? U or C is the key.

38. Parallel Lines L1L1 L2L2 T AB C D E F G H Same-side Interior Angles ? U or C is the key.

39. Parallel Lines L1L1 L2L2 T AB C D E F G H Same-side Interior angles ?

40. Parallel Lines L1L1 L2L2 T AB C D E F G H Same-side exterior angles ?

41. Parallel Lines L1L1 L2L2 T AB C D E F G H Same-side exterior angles ?

42. Parallel Lines L1L1 L2L2 T AB C D E F G H Same-side exterior angles ?

43. Parallel Lines L1L1 L2L2 T AB C D E F G H

44. L1L1 L2L2 T AB C D E F G H

45. Parallel Planes Parallel planes are planes that do not intersect.

46. Lines Parallel to Planes Are lines that do not intersect the plane.

47. Lines Parallel to Planes Are lines that do not intersect the plane.

48. Summary of Lines 1.Lines fall into two categories : Intersecting and Non-intersecting. 2. Intersecting lines are either: Perpendicular or Non-perpendicular

49. 3.Non-intersecting lines are either: Parallel or Skew Coplanar or Non-coplanar Summary of Lines

50. Summary Continued 4.Lines can be parallel to planes by not intersecting the planes and not being in the planes.

51. Summary Continued 5.Parallel planes are planes the do not intersect.

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