1. Parallel Lines and Transversals
Section 3.3 and 3.4

2. Corresponding Angle Postulate
If two parallel lines are cut by a transversal, then the pairs of corresponding angles are congruent. 2 1

3. Alternate Interior Angle Theorem
If two parallel lines are cut by a transversal, then the pairs of alternate interior angles are congruent. 1 2

4. Consecutive Interior or Same Side Interior Angles Theorem
If two parallel lines are cut by a transversal, then the pairs of consecutive interior (same side) angles are supplementary. 4 3

5. Alternate Exterior Angles Theorem
If two lines are cut by a transversal, then the pairs of alternate exterior angles are congruent. 1 2

6. Perpendicular Transversal Theorem
If a transversal is perpendicular to one of two parallel lines, then it is perpendicular to the other.
if t s
then p s s p t

7. Example
What’s A’s relationship to the angle with the measure of 5x -3◦?
Corresponding Angle
Find the m A if x = 10◦.
47◦
What is the name of
B and its measure?
Consecutive Interior or
Same Side Angle, 133◦ A B
5x -3◦

8. Example What is the relationship between A and B? Vertical Angles
What is the relationship between A and C?
Alternate Interior Angles
What is the relationship
between B and 65◦?
Alternate Exterior Angles
What is the m A, m B,
and m C?
m A = 65◦, m B = 65◦, m C = 65◦ A B
65◦ C

9. Corresponding Angle Postulate Converse
If two lines are cut by a transversal so that corresponding angles are congruent, then the lines are parallel. 2 1

10. Alternate Interior Angle Theorem Converse
If two lines are cut by a transversal so that alternate interior angles are congruent, then the lines are parallel. 2 1

11. Consecutive Interior or Same Side Interior Angles Theorem Converse
If two lines are cut by a transversal so that consecutive interior angles are supplementary, then the lines are parallel. 4 3

12. Alternate Exterior Angles Theorem Converse
If two lines are cut by a transversal so that alternate exterior angles are congruent, then the lines are parallel. 1 2

13. Example Find the value of x that makes lines d and f parallel.
x = 6x - 25◦
-5x = -25◦
x = 5◦
6x - 25◦ f x d

14. Example Find the value of x that would make line d and f parallel.
7x = 2x + 95◦
5x = 95◦
x = 19◦ f
2x + 95◦ 7x d

15. Example Find the value of x that would make line d and f parallel.
3x = 2x + 137◦
x = 137◦
2x + 137◦ f 3x d

16. Example Find the value of x that would make line d and f parallel.
4x + 2x - 60◦ = 180◦
6x - 60◦ = 180◦
6x = 240◦
x = 40◦ f 4x
2x - 60◦ d

17. Example Find the value of x that would make line d and f parallel.
4x + 3x - 30◦ = 180◦
7x - 30◦ = 180◦
7x = 210◦
x = 30◦ f 4x
3x - 30◦ d

18. What We Learned Today
When parallel lines are cut by a transversal line, then:
Corresponding Angles are Congruent
Alternate Interior Angles are Congruent
Alternate Exterior Angles are Congruent
Consecutive Interior or Same Side Angles are supplementary
We also learned about the converses of these statements.