1. Lines and Angle Relationships
Section 3.5
Proving Lines Parallel
Lines and Angle Relationships

2. Converse of a Statement
Inter-change the words following the “if” with the words following the “then” in a sentence.
Example: If it rains then the grass grows.
Converse: If the grass grows then it rains.

3. Parallel Postulate:
If given 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.

4. Corresponding s Postulate
If two lines are parallel, then
corresponding <‘s are congruent. 1 2 l m

5. Corresponding s Converse
If 2 lines are cut by a transversal so that corresponding s are , then the lines are .
** If 1  2, then l m. 1 2 l m

7. Alt. Int. s
If 2 lines are parallel, then alternate interior angles are congruent. 1 2 l m

8. Alt. Int. s Converse
If 2 lines are cut by a transversal so that alt. int. s are , then the lines are .
** If 1  2, then l m. 1 2 l m

9. Consecutive Int. s
If 2 lines are parallel, then consecutive interior angles are supplementary (180°). l m 1 2

10. Consecutive Int. s Converse
If 2 lines are cut by a transversal so that consecutive int. s are supplementary, then the lines are .
** If 1 & 2 are supplementary, then l m. l m 1 2

11. Alt. Ext. s
If 2 lines parallel, then alternate exterior angles are congruent. l m 1 2

12. Alt. Ext. s Converse
If 2 lines are cut by a transversal so that alt. ext. s are , then the lines are .
** If 1  2, then l m. l m 1 2

13. Ex: Based on the info in the diagram, is p q ? If so, give a reason.
Yes, alt. ext. s conv. No p q p q p q

14. Ex: Find the value of x that makes j  k .
The angles marked are consecutive interior s.
Therefore, they are supplementary.
x + 3x = 180
4x = 180
x = 45
xo xo
j k

15. Are there any parallel lines
In this bookcase?
How do you know?

17. Assignment: Textbook p. 211, #’s 8 – 21 all