5.3 Congruent Angles Associated With Parallel Lines Objective: 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:.) 1 2

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 b Prove: a b Theorem:If two parallel lines are cut by a transversal, each pair of alternate exterior angles are congruent. (short form:.)

1 5 Given: a ll b Prove: a b Theorem:If two parallel lines are cut by a transversal, each pair of corresponding angles are congruent. (short form:.)

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: 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 b Prove: a b

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: ab 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 c Prove: a ll c a b c

1 3x + 5 If c ll d, find m c d 2x + 10

A B F C D E Given: Prove:

Given: Prove: g h 1 2 3

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

Summary If lines are parallel, name the different ways angles are congruent or supplementary. Homework: worksheet