1. Parallel Lines
With
Transversals

2. These are Parallel LinesV A B V C D

3. Line AB || Line CD V A B V C D

4. This is the transversal

5. This transversal slices and dices 2 parallel lines.

6. When you slice 2 || lines, 8 special angles are formed.1 2 V 3 4 5 6 V 7 8

7. Corresponding Angles
Same Spot
Different Line

8. Corresponding Congruent
Remember…
Corresponding Congruent

9. The line below is a mirror image of the line above it.1 2 V 3 4 5 6 V 7 8

10. 5 is the corresponding angle to 1
5 is the corresponding angle to 1. It is in the same spot on the line below. Corresponding angles are congruent. 1 2 V 3 4 5 6 V 7 8

11. 6 is the corresponding angle to 2
6 is the corresponding angle to 2. It is in the same spot on the line below. Corresponding angles are congruent. 1 2 V 3 4 5 6 V 7 8

12. 7 is the corresponding angle to 3
7 is the corresponding angle to 3. It is in the same spot on the line below. Corresponding angles are congruent. 1 2 V 3 4 5 6 V 7 8

13. ? is the corresponding angle to 4?1 2 V 3 4 5 6 V 7 8

14. Interior Angles
Inside the
Football Field

15. Inside the 2 Parallel Lines.
Interior Angles V V
Inside the 2 Parallel Lines.

16. Remember…
Interior means Inside

17. Interior Angles: The 4 angles in-between the 2 parallel lines.1 2 V 3 4 5 6 V 7 8

18. Same-side
Interior Angles
Are
Hanging Out on
The Same Side of
The Transversal.

19. Same Side Supplemental
Interior Angles
Are
Supplemental
Same Side Supplemental

20. Same Side Supplemental
Remember…
Same Side Supplemental

21. Same-Side Interior Angles: The 2 angles on the same side of the transversal1 2 V 3 4 5 6 V 7 8

22. Same-Side Interior Angles: These 2 are also on the same side of the transversal.1 2 V 3 4 5 6 V 7 8

23. Same-Side Interior Angles: Are SupplementalV 3 5 V
Angle 3 + Angle 5 = 180

24. Example: Same-Side Interior Angles: Are SupplementalV 55 ? V
55 + ? = 180

25. Same-Side Interior Angles: Are SupplementalV 55
125 V
= 180

26. Same-Side Interior Angles: Are SupplementalV 70 x V
70 + x = 180

27. Same-Side Interior Angles: Are SupplementalV 70
X = 110 V
= 180

28. Same-Side = Supplemental
120 + x = 180 V
120 x V
x = 60

29. Alternate
Interior Angles
Are
Congruent
They are the same!

30. Alternate Interior Angles: Are on opposite sides of the the transversal.1 2 V 3 4 5 6 V 7 8

31. Alternate Interior Angles: Are on opposite sides of the the transversal.1 2 V 3 4 5 6 V 7 8

32. Alternate Interior Angles: Are congruent1 2 V 3 4 5 6 V 7 8

33. Alternate Interior Angles: Are congruentV
160 x V
What is x?
x = 160

34. Why? Because they are part of the 2 sets of vertical angles that are congruent1 2 V 3 4 5 6 V 7 8

35. These 2 sets of vertical angles are also congruent1 2 V 3 4 5 6 V 7 8

36. Exterior Angles
Outside the
Football Field

37. External Angles are OUTSIDE the Football Field1 2 V V 7 8

38. And now, time for Dramatic Kitty

39. A Parallel Lines with Transversals Puzzle

40. Find the remaining angle measures.? ? V 50 ? ? ? V ? ?

41. Vertical Angles. ? 50 V 50 ? ? ? V ? ?

42. Corresponding Angles (One Line Below)? 50 V 50 ? 50 ? V 50 ?

43. Same Vertical Angles One Line Below? 50 V 50 ? ? 50 V 50 ?

44. Same Side Supplemental? 50 V 50
130
130 50 V 50 ?

45. (or Alternate Exterior Angles)
Vertical Angles
(or Alternate Exterior Angles)
130 50 V 50
130
130 50 V 50
130

46. A Parallel Lines with Transversals Puzzle
With Algebra

47. Find the value of x. 50 V
X + 1 V

48. Corresponding Angles are Equal.50 V
X + 1 V
X + 1 = 50
X = 49

49. Find the value of x. V
5x - 16
2X + 20 V

50. Alternate Interior Angles are Congruent.V
5x - 16
2X + 20 V
5X - 16 = 2X + 20
X = 12

51. Now try some problems on your own.