1. 3-2 Angles and Parallel Lines1 2 3 4 a b k
Postulate 3.1 Corresponding Angles
If two parallel lines are cut by a transversal, then each pair of corresponding angles is congruent.
There will be four sets of corresponding angles each time two lines are cut.
Refer to the figure above. In the figure a || b, and k is the transversal. Which angle is congruent to 1? Explain your answer.
3, because it is corresponding.

2. Example m 3 + m 4 = 180 m 1 + m 4 = 180 m 1 + 60 = 180 m 1 = 120
Try “Check Your Progress” on page 149, #1
Find the measure of 1, if 4 = 60.
1 corresponds to 3
3 and 4 are a linear pair = 180

3. Theorems 1. 3  6 and 4  5 2. 3 + 5 = 180 and 4 + 6 = 1807 8 6 5 3 4
Theorem 3.1: Alternate Interior Angles – if two parallel lines are cut by a transversal, then each pair of alternate interior angles is congruent.
Theorem 3.2: Consecutive Interior Angles: If two parallel lines are cut by a transversal, then each pair of consecutive interior angles is supplementary.
Theorem 3.3: Alternate Exterior Angles: If two parallel lines are cut by a transversal, then each pair of alternate exterior angles is congruent.
1. 3  6 and 4  5
2. 3 + 5 = 180 and 4 + 6 = 180
3. 1  8 and 2  7

4. Example In the figure above, a || b and k is a transversal. Find m 2.1 2 a b k
(4x – 5)
(3x + 10)
1 + 2 = 180
4x – 5 + 3x + 10 = 180
7x + 5 = 180
7x = 175
x = 25
Are we done?
m 1 = 4(25) – 5
100 – 5 95
m 2 = 3(25) + 10 85
In the figure above, a || b and k is a transversal. Find m 2.
1  4x – 5 and 2  3x + 10
1 and 2 are consecutive interior angles so they are supplementary

5. Theorem 3.4: Perpendicular Transversal
In a plane, if a line is perpendicular to one of two parallel lines, then it is perpendicular to the other.
Example: Use Example #3 (pg. 151) to answer “Check Your Progress” #3.
m2 = 4x + 7 & m3 = 5x –13
4x + 7 = 5x – 13
7 = x – 13
20 = x
m 3 = 5x – 13, so
m 3 = 5(20) – 13
m 3 = 100 – 13
m 3 = 87

6. Proof
Take some time to take look at the proof shown on page Proving Theorem 3.4
Practice Problems: Do #1-6 on page 152 before you begin your homework.