Download Lesson 1, Properties of Parallel Lines

Properties of
Parallel Lines
Geometry
Unit 3, Lesson 1
Mrs. King
Angles Formed by a
Transversal

Transversal – a line that intersects two lines
4
t
1
3 2
L
M
8 5
7 6
Corresponding Angles

Two angles are corresponding angles if they occupy
corresponding positions, such as 1 and 5
t
4
1
3 2
L
M
8 5
7 6
Alternate Interior Angles

Two angles are alternate interior angles if they lie
between L and M on opposite sides of t, such as
2 and 8
t
4
1
3 2
L
M
8 5
7 6
Alternate Exterior Angles

Two angles are alternate exterior angles if they lie
outside L and M on opposite sides of t, such as
1 and 7
t
4
1
3 2
L
M
8 5
7 6
Same-Side-Interior Angles

Two angles are consecutive interior angles if they lie
between L and M on the same side of t, such as
2 and 5
t
4
1
3 2
L
M
8 5
7 6
Transitive Property

If a=b and b=c, then a=c

What does this remind you of?!
Example



Given: 1  3 and 3  5
What can we conclude?
1  5 due to the Transitive Property
Corresponding Angles
Postulate

If two parallel lines are cut by a transversal,
then corresponding angles are congruent.
1  5
2  6
3  7
4  8
Alternate Interior Angles
Theorem

If two parallel lines are cut by a transversal,
then alternate interior angles are congruent.
2  8
3  5
Alternate Exterior Angles
Theorem

If two parallel lines are cut by a transversal,
then alternate exterior angles are congruent.
1  7
4  5
Same-Side Interior Angles
Theorem

If two parallel lines are cut by a
transversal, then same-side
interior angles are supplements.
2 and 5 are supplementary
3 and 8 are supplementary
Find the measure of each
angle given l || m.
42°
l
m
Properties of Parallel Lines
In the diagram above, l || m.
Find the values of a, b, and c.
a = 65
c = 40
a + b + c = 180
65 + b + 40 = 180
b = 75
Angles: