1. Proving Lines Parallel
3-4
Proving Lines Parallel
Objectives:
To recognize angle conditions that produce parallel lines.
To prove two lines are parallel based on given angle relationships..

2. Vocabulary
Parallel Postulate

3. Postulate 3-4
If two lines in a plane are cut by a transversal so that the corresponding angles are congruent, then the lines are parallel.

4. Postulate 3-5 Parallel Postulate
If there is a line and a point not on the line, then there exists exactly one line through the point that is parallel to the given line.

5. Theorem 3-5
If two lines in a plane are cut by a transversal so that a pair of alternate exterior angles are congruent, then the two lines are parallel.

6. Theorem 3-6
If two lines in a plane are cut by a transversal so that a pair of consecutive interior angles is supplementary, then the lines are parallel.

7. Theorem 3-7
If two lines in a plane are cut by a transversal so that a pair of alternate interior angles are congruent, then the lines are parallel.

8. Theorem 3-8
In a plane, if two lines are perpendicular to the same line, then they are parallel.

9. Example 1

10. Example 2

11. Example 3

12. Homework
3-4 Worksheet