1. 5.2 Proving That Lines Are Parallel
Advanced Geometry
5.2 Proving That Lines Are Parallel
Learner Objective: Students will apply the Exterior Angle theorem and will use angles formed by 
 a transversal to prove that lines are parallel.
Learner Objective: Students will be able to use angles formed by a 
 transversal to prove that two lines are parallel.
MA-HS-3.1.3
 Students will analyze and apply angle relationships (e.g., linear pairs, vertical, complementary, 
 supplementary, corresponding and alternate interior angles) in real-world and mathematical 
 situations.

2. Given: M is the midpoint of
Learner Objective: Students will apply the Exterior Angle theorem and will use angles formed by 
 a transversal to prove that lines are parallel.
Warm-Up
Given: M is the midpoint of
Prove: K N W L M

3. Learner Objective: Students will apply the Exterior Angle theorem and will use angles formed by 
 a transversal to prove that lines are parallel.
Given lines m and n cut by transversal t:
Name the pairs of alternate interior angles.
Name the pairs of corresponding angles.
Name the pairs of alternate exterior angles.
Name pairs of angles that are interior angles on 
the same side of the transversal.
Name pairs of angles that are exterior angles on 
the same side of the transversal. 2 1 3 4 5 6 7 8 m n t

4. Exterior Angle of a triangle
Learner Objective: Students will apply the Exterior Angle theorem and will use angles formed by 
 a transversal to prove that lines are parallel.
Exterior Angle of a triangle
An Exterior Angle of a triangle is formed whenever a sided 
of the triangle is extended to form an angle supplementary 
to the adjacent interior angle. A B C D
Remote Interior
Angles
Exterior Angle
The other two interior 
angles are referred to as 
Remote Interior Angles.
Adjacent Interior Angle

5. Exterior Angle Inequality Theorem
Learner Objective: Students will apply the Exterior Angle theorem and will use angles formed by 
 a transversal to prove that lines are parallel.
Exterior Angle Inequality Theorem
The measure of an exterior angle of a triangle is greater 
than the measure of either remote interior angle. A B C D

6. Learner Objective: Students will be able to use angles formed by a transversal to prove that two lines 
 are parallel.
Learner Objective: Students will apply the Exterior Angle theorem and will use angles formed by 
 a transversal to prove that lines are parallel.

7. Learner Objective: Students will be able to use angles formed by a transversal to prove that two lines 
 are parallel.
Learner Objective: Students will apply the Exterior Angle theorem and will use angles formed by 
 a transversal to prove that lines are parallel.

8. Learner Objective: Students will be able to use angles formed by a transversal to prove that two lines 
 are parallel.
Learner Objective: Students will apply the Exterior Angle theorem and will use angles formed by 
 a transversal to prove that lines are parallel.

9. Learner Objective: Students will be able to use angles formed by a transversal to prove that two lines 
 are parallel.
Learner Objective: Students will apply the Exterior Angle theorem and will use angles formed by 
 a transversal to prove that lines are parallel.

10. Learner Objective: Students will be able to use angles formed by a transversal to prove that two lines 
 are parallel.
Learner Objective: Students will apply the Exterior Angle theorem and will use angles formed by 
 a transversal to prove that lines are parallel.

11. Learner Objective: Students will be able to use angles formed by a transversal to prove that two lines 
 are parallel.
Learner Objective: Students will apply the Exterior Angle theorem and will use angles formed by 
 a transversal to prove that lines are parallel.

12. Learner Objective: Students will apply the Exterior Angle theorem and will use angles formed by 
 a transversal to prove that lines are parallel.

13. Learner Objective: Students will apply the Exterior Angle theorem and will use angles formed by 
 a transversal to prove that lines are parallel.

14. Learner Objective: Students will apply the Exterior Angle theorem and will use angles formed by 
 a transversal to prove that lines are parallel.

15. Learner Objective: Students will apply the Exterior Angle theorem and will use angles formed by 
 a transversal to prove that lines are parallel.

16. Learner Objective: Students will apply the Exterior Angle theorem and will use angles formed by 
 a transversal to prove that lines are parallel.

17. Learner Objective: Students will apply the Exterior Angle theorem and will use angles formed by 
 a transversal to prove that lines are parallel.

18. Learner Objective: Students will apply the Exterior Angle theorem and will use angles formed by 
 a transversal to prove that lines are parallel.

19. Learner Objective: Students will apply the Exterior Angle theorem and will use angles formed by 
 a transversal to prove that lines are parallel.

20. Learner Objective: Students will apply the Exterior Angle theorem and will use angles formed by 
 a transversal to prove that lines are parallel.

21. Learner Objective: Students will apply the Exterior Angle theorem and will use angles formed by 
 a transversal to prove that lines are parallel.

22. Learner Objective: Students will apply the Exterior Angle theorem and will use angles formed by 
 a transversal to prove that lines are parallel.

23. Learner Objective: Students will apply the Exterior Angle theorem and will use angles formed by 
 a transversal to prove that lines are parallel.

24. Learner Objective: Students will apply the Exterior Angle theorem and will use angles formed by 
 a transversal to prove that lines are parallel.

25. Learner Objective: Students will apply the Exterior Angle theorem and will use angles formed by 
 a transversal to prove that lines are parallel.

26. Learner Objective: Students will apply the Exterior Angle theorem and will use angles formed by 
 a transversal to prove that lines are parallel.

27. Learner Objective: Students will apply the Exterior Angle theorem and will use angles formed by 
 a transversal to prove that lines are parallel.

28. Learner Objective: Students will apply the Exterior Angle theorem and will use angles formed by 
 a transversal to prove that lines are parallel.

29. Learner Objective: Students will apply the Exterior Angle theorem and will use angles formed by 
 a transversal to prove that lines are parallel.

30. Learner Objective: Students will apply the Exterior Angle theorem and will use angles formed by 
 a transversal to prove that lines are parallel.

31. Learner Objective: Students will apply the Exterior Angle theorem and will use angles formed by 
 a transversal to prove that lines are parallel.

32. Learner Objective: Students will apply the Exterior Angle theorem and will use angles formed by 
 a transversal to prove that lines are parallel.

33. Learner Objective: Students will apply the Exterior Angle theorem and will use angles formed by 
 a transversal to prove that lines are parallel.

34. Learner Objective: Students will apply the Exterior Angle theorem and will use angles formed by 
 a transversal to prove that lines are parallel.

35. Learner Objective: Students will apply the Exterior Angle theorem and will use angles formed by 
 a transversal to prove that lines are parallel.

36. Learner Objective: Students will apply the Exterior Angle theorem and will use angles formed by 
 a transversal to prove that lines are parallel.

37. Learner Objective: Students will apply the Exterior Angle theorem and will use angles formed by 
 a transversal to prove that lines are parallel.

38. Learner Objective: Students will apply the Exterior Angle theorem and will use angles formed by 
 a transversal to prove that lines are parallel.

39. Learner Objective: Students will apply the Exterior Angle theorem and will use angles formed by 
 a transversal to prove that lines are parallel.

40. Learner Objective: Students will apply the Exterior Angle theorem and will use angles formed by 
 a transversal to prove that lines are parallel.

41. Learner Objective: Students will apply the Exterior Angle theorem and will use angles formed by 
 a transversal to prove that lines are parallel.

42. Learner Objective: Students will apply the Exterior Angle theorem and will use angles formed by 
 a transversal to prove that lines are parallel.

43. Learner Objective: Students will apply the Exterior Angle theorem and will use angles formed by 
 a transversal to prove that lines are parallel.

44. Learner Objective: Students will apply the Exterior Angle theorem and will use angles formed by 
 a transversal to prove that lines are parallel.

45. Learner Objective: Students will apply the Exterior Angle theorem and will use angles formed by 
 a transversal to prove that lines are parallel.

46. Learner Objective: Students will apply the Exterior Angle theorem and will use angles formed by 
 a transversal to prove that lines are parallel.

47. Learner Objective: Students will be able to use angles formed by a transversal to prove that two lines 
 are parallel.

48. Learner Objective: Students will be able to use angles formed by a transversal to prove that two lines 
 are parallel.

49. Learner Objective: Students will be able to use angles formed by a transversal to prove that two lines 
 are parallel.

50. Learner Objective: Students will be able to use angles formed by a transversal to prove that two lines 
 are parallel.

51. Learner Objective: Students will be able to use angles formed by a transversal to prove that two lines 
 are parallel.

52. Learner Objective: Students will be able to use angles formed by a transversal to prove that two lines 
 are parallel.

53. Learner Objective: Students will be able to use angles formed by a transversal to prove that two lines 
 are parallel.

54. Learner Objective: Students will be able to use angles formed by a transversal to prove that two lines 
 are parallel.

55. Learner Objective: Students will be able to use angles formed by a transversal to prove that two lines 
 are parallel.

56. Learner Objective: Students will be able to use angles formed by a transversal to prove that two lines 
 are parallel.

57. Learner Objective: Students will be able to use angles formed by a transversal to prove that two lines 
 are parallel.

58. Learner Objective: Students will be able to use angles formed by a transversal to prove that two lines 
 are parallel.

59. Learner Objective: Students will be able to use angles formed by a transversal to prove that two lines 
 are parallel.

60. Learner Objective: Students will be able to use angles formed by a transversal to prove that two lines 
 are parallel.

61. Learner Objective: Students will be able to use angles formed by a transversal to prove that two lines 
 are parallel.

62. Learner Objective: Students will be able to use angles formed by a transversal to prove that two lines 
 are parallel.

63. Name: _______________________
State the theorem that proves lines a and b or lines c and d parallel.
1. __________________________
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2. __________________________
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3. __________________________
__________________________
4. __________________________
__________________________
5. __________________________
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