This document defines key vocabulary terms related to parallel lines and transversals, including parallel lines, transversals, interior angles, exterior angles, alternate interior angles, same-side interior angles, alternate exterior angles, and corresponding angles. It provides examples of how these terms apply when two parallel lines are intersected by a transversal, and lists the parallel line postulates that corresponding angles and alternate interior angles are congruent if lines are parallel.

1. SECTION 5-3
Parallel Lines and Transversals

2. ESSENTIAL QUESTIONS
How do you identify angles formed by parallel lines
and transversals?
How do you identify and use properties of parallel
lines?
Where you’ll see this:
Construction, safety, navigation, music

3. VOCABULARY
1. Parallel Lines:
2. Parallel Planes:
3. Skew Lines:
4. Transversal:
5. Interior Angles:
6. Exterior Angles:

4. VOCABULARY
1. Parallel Lines: Coplanar lines that do not intersect
2. Parallel Planes:
3. Skew Lines:
4. Transversal:
5. Interior Angles:
6. Exterior Angles:

5. VOCABULARY
1. Parallel Lines: Coplanar lines that do not intersect
2. Parallel Planes: Planes that do not intersect
3. Skew Lines:
4. Transversal:
5. Interior Angles:
6. Exterior Angles:

6. VOCABULARY
1. Parallel Lines: Coplanar lines that do not intersect
2. Parallel Planes: Planes that do not intersect
3. Skew Lines: Noncoplanar lines that do not intersect and are
not parallel
4. Transversal:
5. Interior Angles:
6. Exterior Angles:

7. VOCABULARY
1. Parallel Lines: Coplanar lines that do not intersect
2. Parallel Planes: Planes that do not intersect
3. Skew Lines: Noncoplanar lines that do not intersect and are
not parallel
4. Transversal: A line that intersects two other coplanar lines at
different points
5. Interior Angles:
6. Exterior Angles:

8. VOCABULARY
1. Parallel Lines: Coplanar lines that do not intersect
2. Parallel Planes: Planes that do not intersect
3. Skew Lines: Noncoplanar lines that do not intersect and are
not parallel
4. Transversal: A line that intersects two other coplanar lines at
different points
5. Interior Angles: Angles formed in between two coplanar lines
when intersected by a transversal
6. Exterior Angles:

9. VOCABULARY
1. Parallel Lines: Coplanar lines that do not intersect
2. Parallel Planes: Planes that do not intersect
3. Skew Lines: Noncoplanar lines that do not intersect and are
not parallel
4. Transversal: A line that intersects two other coplanar lines at
different points
5. Interior Angles: Angles formed in between two coplanar lines
when intersected by a transversal
6. Exterior Angles: Angles formed outside two coplanar lines
when intersected by a transversal

10. VOCABULARY
7. Alternate Interior Angles:
8. Same-side Interior Angles:
9. Alternate Exterior Angles:
10. Corresponding Angles:

11. VOCABULARY
7. Alternate Interior Angles: Interior angles on opposite sides of a
transversal; these angles are congruent
8. Same-side Interior Angles:
9. Alternate Exterior Angles:
10. Corresponding Angles:

12. VOCABULARY
7. Alternate Interior Angles: Interior angles on opposite sides of a
transversal; these angles are congruent
8. Same-side Interior Angles: Interior angles on the same side of a
transversal; these angles are supplementary
9. Alternate Exterior Angles:
10. Corresponding Angles:

13. VOCABULARY
7. Alternate Interior Angles: Interior angles on opposite sides of a
transversal; these angles are congruent
8. Same-side Interior Angles: Interior angles on the same side of a
transversal; these angles are supplementary
9. Alternate Exterior Angles: Exterior angles on opposite sides of a
transversal; these angles are congruent
10. Corresponding Angles:

14. VOCABULARY
7. Alternate Interior Angles: Interior angles on opposite sides of a
transversal; these angles are congruent
8. Same-side Interior Angles: Interior angles on the same side of a
transversal; these angles are supplementary
9. Alternate Exterior Angles: Exterior angles on opposite sides of a
transversal; these angles are congruent
10. Corresponding Angles: These angles will have the same
position around a transversal and the lines it intersects
with; these angles are congruent

15. m
a 1 2
3 4
b 5 6
7 8

16. m
a 1 2
3 4
b 5 6
7 8
Interior Angles:

17. m
a 1 2
3 4
b 5 6
7 8
Interior Angles: 3, 4, 5, 6

18. m
a 1 2
3 4
b 5 6
7 8
Interior Angles: 3, 4, 5, 6
Exterior Angles:

19. m
a 1 2
3 4
b 5 6
7 8
Interior Angles: 3, 4, 5, 6
Exterior Angles: 1, 2, 7, 8

20. m
a 1 2
3 4
b 5 6
7 8
Interior Angles: 3, 4, 5, 6 Alternate Interior Angles:
Exterior Angles: 1, 2, 7, 8

21. m
a 1 2
3 4
b 5 6
7 8
Interior Angles: 3, 4, 5, 6 Alternate Interior Angles: 3 & 6, 4 & 5
Exterior Angles: 1, 2, 7, 8

22. m
a 1 2
3 4
b 5 6
7 8
Interior Angles: 3, 4, 5, 6 Alternate Interior Angles: 3 & 6, 4 & 5
Exterior Angles: 1, 2, 7, 8 Same-side Interior Angles:

23. m
a 1 2
3 4
b 5 6
7 8
Interior Angles: 3, 4, 5, 6 Alternate Interior Angles: 3 & 6, 4 & 5
Exterior Angles: 1, 2, 7, 8 Same-side Interior Angles: 3 & 5, 4 & 6

24. m
a 1 2
3 4
b 5 6
7 8
Interior Angles: 3, 4, 5, 6 Alternate Interior Angles: 3 & 6, 4 & 5
Exterior Angles: 1, 2, 7, 8 Same-side Interior Angles: 3 & 5, 4 & 6
Alternate Exterior Angles:

25. m
a 1 2
3 4
b 5 6
7 8
Interior Angles: 3, 4, 5, 6 Alternate Interior Angles: 3 & 6, 4 & 5
Exterior Angles: 1, 2, 7, 8 Same-side Interior Angles: 3 & 5, 4 & 6
Alternate Exterior Angles: 1 & 8, 2 & 7

26. m
a 1 2
3 4
b 5 6
7 8
Interior Angles: 3, 4, 5, 6 Alternate Interior Angles: 3 & 6, 4 & 5
Exterior Angles: 1, 2, 7, 8 Same-side Interior Angles: 3 & 5, 4 & 6
Alternate Exterior Angles: 1 & 8, 2 & 7
Corresponding Angles:

27. m
a 1 2
3 4
b 5 6
7 8
Interior Angles: 3, 4, 5, 6 Alternate Interior Angles: 3 & 6, 4 & 5
Exterior Angles: 1, 2, 7, 8 Same-side Interior Angles: 3 & 5, 4 & 6
Alternate Exterior Angles: 1 & 8, 2 & 7
Corresponding Angles: 1 & 5, 2 & 6, 3 & 7, 4 & 8

28. Parallel Line Postulates

29. Parallel Line Postulates
If two parallel lines are intersected by a transversal,
then corresponding angles are congruent

30. Parallel Line Postulates
If two parallel lines are intersected by a transversal,
then corresponding angles are congruent
If two lines are intersected by a transversal so that
corresponding angles are congruent, then the lines are
parallel

31. EXAMPLE 1
sur sur
u u
In the figure, AB PCD. If m∠AEF = (4x +10)° and
m∠EFD = (2x + 20)°, find m∠AEF.
G
A B
E
C F D
H

32. EXAMPLE 1
sur sur
u u
In the figure, AB PCD. If m∠AEF = (4x +10)° and
m∠EFD = (2x + 20)°, find m∠AEF.
G
A B
* E
C F D
H

33. EXAMPLE 1
sur sur
u u
In the figure, AB PCD. If m∠AEF = (4x +10)° and
m∠EFD = (2x + 20)°, find m∠AEF.
G
A B
* E
C F
* D
H

34. EXAMPLE 1
sur sur
u u
In the figure, AB PCD. If m∠AEF = (4x +10)° and
m∠EFD = (2x + 20)°, find m∠AEF.
G
4x +10 = 2x + 20
A B
* E
C F
* D
H

35. EXAMPLE 1
sur sur
u u
In the figure, AB PCD. If m∠AEF = (4x +10)° and
m∠EFD = (2x + 20)°, find m∠AEF.
G
4x +10 = 2x + 20
−2x −2x
A B
* E
C F
* D
H

36. EXAMPLE 1
sur sur
u u
In the figure, AB PCD. If m∠AEF = (4x +10)° and
m∠EFD = (2x + 20)°, find m∠AEF.
G
4x +10 = 2x + 20
−2x −10 −2x −10
A B
* E
C F
* D
H

37. EXAMPLE 1
sur sur
u u
In the figure, AB PCD. If m∠AEF = (4x +10)° and
m∠EFD = (2x + 20)°, find m∠AEF.
G
4x +10 = 2x + 20
−2x −10 −2x −10
2x = 10
A B
* E
C F
* D
H

38. EXAMPLE 1
sur sur
u u
In the figure, AB PCD. If m∠AEF = (4x +10)° and
m∠EFD = (2x + 20)°, find m∠AEF.
G
4x +10 = 2x + 20
−2x −10 −2x −10
2x = 10
A B
* E
2 2
C F
* D
H

39. EXAMPLE 1
sur sur
u u
In the figure, AB PCD. If m∠AEF = (4x +10)° and
m∠EFD = (2x + 20)°, find m∠AEF.
G
4x +10 = 2x + 20
−2x −10 −2x −10
2x = 10
A B
* E
2 2
C F
* D
x=5
H

40. EXAMPLE 1
sur sur
u u
In the figure, AB PCD. If m∠AEF = (4x +10)° and
m∠EFD = (2x + 20)°, find m∠AEF.
G
4x +10 = 2x + 20
−2x −10 −2x −10
2x = 10
A B
* E
2 2
C F
* D
x=5
m∠AEF = (4(5) +10)°
H

41. EXAMPLE 1
sur sur
u u
In the figure, AB PCD. If m∠AEF = (4x +10)° and
m∠EFD = (2x + 20)°, find m∠AEF.
G
4x +10 = 2x + 20
−2x −10 −2x −10
2x = 10
A B
* E
2 2
C F
* D
x=5
m∠AEF = (4(5) +10)°
H
m∠AEF = 30°

42. EXAMPLE 2
sur sur
u u
In the figure, AB PCD. If m∠FEB = (7x + 40)° and
m∠HFD = (2x + 20)°, find m∠BEF.
G
A B
E
C F D
H

43. EXAMPLE 2
sur sur
u u
In the figure, AB PCD. If m∠FEB = (7x + 40)° and
m∠HFD = (2x + 20)°, find m∠BEF.
G
A B
E
*
C F D
H

44. EXAMPLE 2
sur sur
u u
In the figure, AB PCD. If m∠FEB = (7x + 40)° and
m∠HFD = (2x + 20)°, find m∠BEF.
G
A B
E
*
C F
* D
H

45. EXAMPLE 2
sur sur
u u
In the figure, AB PCD. If m∠FEB = (7x + 40)° and
m∠HFD = (2x + 20)°, find m∠BEF.
G
7x + 40 = 2x + 20
A B
E
*
C F
* D
H

46. EXAMPLE 2
sur sur
u u
In the figure, AB PCD. If m∠FEB = (7x + 40)° and
m∠HFD = (2x + 20)°, find m∠BEF.
G
7x + 40 = 2x + 20
−2x −2x
A B
E
*
C F
* D
H

47. EXAMPLE 2
sur sur
u u
In the figure, AB PCD. If m∠FEB = (7x + 40)° and
m∠HFD = (2x + 20)°, find m∠BEF.
G
7x + 40 = 2x + 20
−2x −40 −2x −40
A B
E
*
C F
* D
H

48. EXAMPLE 2
sur sur
u u
In the figure, AB PCD. If m∠FEB = (7x + 40)° and
m∠HFD = (2x + 20)°, find m∠BEF.
G
7x + 40 = 2x + 20
−2x −40 −2x −40
5x = −20
A B
E
*
C F
* D
H

49. EXAMPLE 2
sur sur
u u
In the figure, AB PCD. If m∠FEB = (7x + 40)° and
m∠HFD = (2x + 20)°, find m∠BEF.
G
7x + 40 = 2x + 20
−2x −40 −2x −40
5x = −20
A B
E
*
5 5
C F
* D
H

50. EXAMPLE 2
sur sur
u u
In the figure, AB PCD. If m∠FEB = (7x + 40)° and
m∠HFD = (2x + 20)°, find m∠BEF.
G
7x + 40 = 2x + 20
−2x −40 −2x −40
5x = −20
A B
E
*
5 5
x = −4
C F
* D
H

51. EXAMPLE 2
sur sur
u u
In the figure, AB PCD. If m∠FEB = (7x + 40)° and
m∠HFD = (2x + 20)°, find m∠BEF.
G
7x + 40 = 2x + 20
−2x −40 −2x −40
5x = −20
A B
E
*
5 5
x = −4
C F
* D
m∠BEF = (7(−4) + 40)°
H

52. EXAMPLE 2
sur sur
u u
In the figure, AB PCD. If m∠FEB = (7x + 40)° and
m∠HFD = (2x + 20)°, find m∠BEF.
G
7x + 40 = 2x + 20
−2x −40 −2x −40
5x = −20
A B
E
*
5 5
x = −4
C F
* D
m∠BEF = (7(−4) + 40)°
H
m∠BEF = 12°

53. EXAMPLE 3
Refer to the figure. For each type of angle relationship
mentioned, list a pair of angles that would satisfy the
relationship.
For example, ∠1 and ∠2 are supplementary.
Complementary:
1 2
3 4
5 6
Supplementary:
7 8

54. EXAMPLE 3
Refer to the figure. For each type of angle relationship
mentioned, list a pair of angles that would satisfy the
relationship.
For example, ∠1 and ∠2 are supplementary.
Complementary:
3
1
4
2
None
5 6
Supplementary:
7 8

55. EXAMPLE 3
Refer to the figure. For each type of angle relationship
mentioned, list a pair of angles that would satisfy the
relationship.
For example, ∠1 and ∠2 are supplementary.
Complementary:
3
1
4
2
None
5 6
Supplementary:
7 8
∠2 and ∠4

56. EXAMPLE 3
Refer to the figure. For each type of angle relationship
mentioned, list a pair of angles that would satisfy the
relationship.
For example, ∠1 and ∠2 are supplementary.
Vertical:
1 2
3 4
5 6
Adjacent:
7 8

57. EXAMPLE 3
Refer to the figure. For each type of angle relationship
mentioned, list a pair of angles that would satisfy the
relationship.
For example, ∠1 and ∠2 are supplementary.
Vertical:
1 2
3 4
5 6
Adjacent:
7 8
∠2 and ∠4

58. EXAMPLE 3
Refer to the figure. For each type of angle relationship
mentioned, list a pair of angles that would satisfy the
relationship.
For example, ∠1 and ∠2 are supplementary.
Vertical:
3
1
4
2
∠1 and ∠4
5 6
Adjacent:
7 8
∠2 and ∠4

59. EXAMPLE 3
Refer to the figure. For each type of angle relationship
mentioned, list a pair of angles that would satisfy the
relationship.
For example, ∠1 and ∠2 are supplementary.
Interior:
1 2
3 4
5 6
Alternate Interior:
7 8

60. EXAMPLE 3
Refer to the figure. For each type of angle relationship
mentioned, list a pair of angles that would satisfy the
relationship.
For example, ∠1 and ∠2 are supplementary.
Interior:
1 2
3 4
5 6
Alternate Interior:
7 8
∠3 and ∠6

61. EXAMPLE 3
Refer to the figure. For each type of angle relationship
mentioned, list a pair of angles that would satisfy the
relationship.
For example, ∠1 and ∠2 are supplementary.
Interior:
3
1
4
2
∠3 and ∠4
5 6
Alternate Interior:
7 8
∠3 and ∠6

62. EXAMPLE 3
Refer to the figure. For each type of angle relationship
mentioned, list a pair of angles that would satisfy the
relationship.
For example, ∠1 and ∠2 are supplementary.
Same-side Interior:
1 2
3 4
5 6
Exterior:
7 8

63. EXAMPLE 3
Refer to the figure. For each type of angle relationship
mentioned, list a pair of angles that would satisfy the
relationship.
For example, ∠1 and ∠2 are supplementary.
Same-side Interior:
1 2
3 4
5 6
Exterior:
7 8
∠1 and ∠7

64. EXAMPLE 3
Refer to the figure. For each type of angle relationship
mentioned, list a pair of angles that would satisfy the
relationship.
For example, ∠1 and ∠2 are supplementary.
Same-side Interior:
3
1
4
2
∠3 and ∠5
5 6
Exterior:
7 8
∠1 and ∠7

65. EXAMPLE 3
Refer to the figure. For each type of angle relationship
mentioned, list a pair of angles that would satisfy the
relationship.
For example, ∠1 and ∠2 are supplementary.
Alternate Exterior:
1 2
3 4
5 6
Corresponding:
7 8

66. EXAMPLE 3
Refer to the figure. For each type of angle relationship
mentioned, list a pair of angles that would satisfy the
relationship.
For example, ∠1 and ∠2 are supplementary.
Alternate Exterior:
1 2
3 4
5 6
Corresponding:
7 8
∠1 and ∠5

67. EXAMPLE 3
Refer to the figure. For each type of angle relationship
mentioned, list a pair of angles that would satisfy the
relationship.
For example, ∠1 and ∠2 are supplementary.
Alternate Exterior:
3
1
4
2
∠1 and ∠8
5 6
Corresponding:
7 8
∠1 and ∠5

68. HOMEWORK

69. HOMEWORK
p. 204 #1-35 odd
“The talent of success is nothing more than doing what you can do,
well.” - Henry W. Longfellow