Proving Lines Parallel

1. Proving Lines Parallel Section 3-5

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

3. Parallel Line Theorems (3.5-3.8) • 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.

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

5. 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.

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

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

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

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

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