5.3 Congruent Angles Associated With Parallel

LinesObjective:

After studying this section, you will be able to:

a. apply the parallel postulate, b. identify the pairs of angles formed by a

transversal cutting parallel lines, and c. apply six theorems about parallel lines.

Postulate: Through a point not on a line there is exactly one parallel to the given line.

P

Theorem: If two parallel lines are cut by a transversal, each pair of

alternate interior angles are congruent.

(short form: .)

lines alt. int. sll

12

Theorem: If two parallel lines are cut by a transversal, then any pair of

angles formed are either congruent or supplementary.

x

1

8

Given: a ll bProve: 1 8

a

b

Theorem: If two parallel lines are cut by a transversal, each pair of

alternate exterior angles are congruent.

(short form: .)

lines alt. ext. sll

1

5

Given: a ll bProve: 1 5

a

b

Theorem: If two parallel lines are cut by a transversal, each pair of corresponding angles are

congruent.

(short form: .) lines corr. sll

Theorem: If two parallel lines are cut by a transversal, each pair of

interior angles on the same side of the transversal are supplementary.

4

6

Prove: 6 ary tosupplement 4 a

b

Given: a ll b

Theorem: If two parallel lines are cut by a transversal each pair of

exterior angles on the same side of the transversal are supplementary.

2

8

Given: a ll bProve:

a

b8 ary tosupplement 2

Theorem: In a plane, if a line is perpendicular to one of two parallel lines, it is perpendicular to the other.

Given: a ll b

Prove:

a b

b c c

a c

Theorem: If two lines are parallel to a third line, they are parallel to each other.

(Transitive property of Parallel Lines)

Given: a ll b, b ll cProve: a ll c

a

b

c

13x + 5

If c ll d, find m 1

c

d 2x + 10

AB

F

C D

E

Given:

Prove:

FA DEFA DEAB CDF E

Given:

Prove:

g h1 supplementary 2

g

h

1

23

a

b

1 C

100

40

If a ll b, find m 1Hint: use the parallel postulate to start

Summary

If lines are parallel, name the different ways angles are congruent or supplementary.

Homework: worksheet