Properties of Parallel Lines

GeometryUnit 3, Lesson 1

Mrs. King

Angles Formed by a Transversal Transversal – a line that intersects two lines

t

L

M

123

4

5

67

8

Corresponding Angles Two angles are corresponding angles if they occupy

corresponding positions, such as 1 and 5

t

L

M

123

4

5

67

8

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

L

M

123

4

5

67

8

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

L

M

123

4

5

67

8

Same-Side-Interior Angles Two angles are consecutive interior angles if they lie

between L and M on the same side of t, such as2 and 5

t

L

M

123

4

5

67

8

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 52 63 74 8

Alternate Interior Angles Theorem If two parallel lines are cut by a transversal,

then alternate interior angles are congruent.

2 83 5

Alternate Exterior Angles Theorem If two parallel lines are cut by a transversal,

then alternate exterior angles are congruent.

1 74 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 supplementary3 and 8 are supplementary

Find the measure of each angle given l || m.

42° l

m

a = 65c = 40

a + b + c = 18065 + b + 40 = 180

b = 75

In the diagram above, l || m.Find the values of a, b, and c.

Properties of Parallel Lines

Angles: