Proving Lines Parallel Section 3-5

Postulate 3.4 If 2 lines are cut by a transversal so that corresponding angles are congruent, then the lines are parallel. 60

Parallel Line Theorems ( ) If 2 lines in a plane are cut by a transversal so that a pair of alternate exterior angles is congruent, then the lines are parallel. If 2 lines in a plane are cut by a transversal so that a pair of consecutive interior angles is supplementary, then the lines are parallel. If 2 lines in a plane are cut by a transversal so that a pair of alternate interior angles is congruent, then the lines are parallel.

In a plane, if 2 lines are perpendicular to the same line, then they are parallel.

Postulates Through a point outside a line, there is exactly one line parallel to the given line. Through a point outside a line, there is exactly one line perpendicular ot the given line.

Theorem 2 lines parallel to a 3 rd line are parallel to each other.

Ways to Prove 2 Lines Parallel 1.Show that a pair of corresponding angles are congruent. 2.Show that a pair of alternate interior angles are congruent. 3.Show that a pair of alternate exterior angles are congruent. 4.Show that a pair of consecutive interior angles are supplementary.

5.In a plane, show that both lines are perpendicular to a 3 rd line. 6.Show that both lines are parallel to a 3 rd line.

Joke Time How do you know when it’s raining cats and dogs? When you step in a poodle!

Why did the apple go out with a fig? Because it couldn’t find a date