3.2 Properties of
Parallel Lines
Objectives: TSW …
• Use the properties of parallel lines cut by a
transversal to determine angles measures.
• Use algebra to find angle measure.
Postulate 3.1
Corresponding Angles Postulate


If a transversal intersects two parallel lines,
then corresponding angles are congruent.
1  5, 2  6, 3  7, 4  8
p
1 2
3 4
5 6
7 8
m
n
Example 1:
In the figure, x ‖ y and m10 = 120. Find m14.
Theorem 3.1:
Alternate Interior Angles Theorem


If a transversal intersects two parallel lines, then
alternate interior angles are congruent.
4  5, 3  6
p
1 2
3 4
5 6
7 8
m
n
Example 2:
In the figure, x ‖ y and m12 = 38. Find m15.
Theorem 3.2:
Same-Side Interior Angles Theorem

If a transversal intersects two parallel lines,
then Same Side Interior Angles are supplementary.

m4 + m6 = 180, m3 + m5 = 180
p
1 2
3 4
5 6
7 8
m
n
Example 3:
In the figure, x ‖ y and m12 = 43. Find m14.
Theorem 3.3:
Alternate Exterior Angles Theorem


If a transversal intersects two parallel lines, then
alternate exterior angles are congruent.
1  8, 2  7
p
1 2
3 4
5 6
7 8
m
n
Example 4:
In the figure, x ‖ y and m11 = 51. Find m16.
Example 5: Finding measures
of Angles
What are the measures of all numbered angles.
Which theorem or postulate justifies each answer?
Example 6:
What is the measure of RTV?
Example 7:
If m5 = 2x – 10, m6 = 4(y – 25), and
m7 = x + 15, find x and y.
Example 8:
In the figure, m3 = 110 and m12 = 55.
Find the measure of the other angles.
Summary
Relationship of angle measures formed by two
parallel lines cut by a transversal.

Corresponding Angles - congruent

Alternate Interior Angles - congruent

Alternate Exterior Angles - congruent
Same Side Interior Angles - Supplementary
