This document contains notes from a geometry lesson on proving lines are parallel. It includes the converse of several postulates about corresponding angles, alternate interior angles, alternate exterior angles, and consecutive interior angles being congruent or supplementary when lines are cut by a transversal. Examples and guided practice are provided to help students understand how to use these converses to prove lines are parallel. The document also references homework problems for further practice in proving parallel lines.

1. 3.3 Prove Parallel Lines
HW pg. 165 #4­14 even, 29­31, 34, 35
September 26, 2014
Bellwork
With your partner, stand in the center of
the room according to the angle pair card
you receive.
Determine whether your angles are
congruent or supplementary.
One partner is to hold the angle pair card,
and the other partner will hold the = card,
(located on the front desk).

2. 3.3 Prove Parallel Lines
HW pg. 165 #4­14 even, 29­31, 34, 35
September 26, 2014
3.3 Prove Lines are Parallel
Postulate 16: Corresponding Angles Converse
If 2 lines are cut by a transversal so the corresponding
angles are congruent, then the lines are parallel.
Example 1
Find the value of x that makes m // n.
Guided Practice #1 with partners
m
n65
(3x + 5)
6 k
2 j
j // k

3. 3.3 Prove Parallel Lines
HW pg. 165 #4­14 even, 29­31, 34, 35
September 26, 2014
Theorem 3.4: Alternate Interior Angles Converse
If 2 lines are cut by a transversal so the alternate interior
angles are congruent, then the lines are parallel.
Theorem 3.5: Alternate Exterior Angles Converse
If 2 lines are cut by a transversal so the alternate exterior
angles are congruent, then the lines are parallel.
Theorem 3.6: Consecutive Interior Angles Converse
If 2 lines are cut by a transversal so the consecutive
interior angles are supplementary, then the lines are parallel.
k
45
jj // k
j // k
j // k
j
k
1
8
3
5
j
k
<3+<5=180

4. 3.3 Prove Parallel Lines
HW pg. 165 #4­14 even, 29­31, 34, 35
September 26, 2014

5. 3.3 Prove Parallel Lines
HW pg. 165 #4­14 even, 29­31, 34, 35
September 26, 2014

6. 3.3 Prove Parallel Lines
HW pg. 165 #4­14 even, 29­31, 34, 35
September 26, 2014
Paragraph Proof: written in paragraph form and in sentences
explaining the logical flow of argument

7. 3.3 Prove Parallel Lines
HW pg. 165 #4­14 even, 29­31, 34, 35
September 26, 2014
Theorem 3.7: Transitive Property of Parallel Lines
If 2 lines are parallel to the same line,
then they are parallel to each other.

8. 3.3 Prove Parallel Lines
HW pg. 165 #4­14 even, 29­31, 34, 35
September 26, 2014
HW pg. 165
#4­14 evens
29­31,
34 & 35