1. Chapter 3: Parallel and Perpendicular Lines
Section 3.3: Prove Lines are Parallel

2. Section 3.3: Prove Lines are Parallel
Goal: Show that two lines are parallel.

3. Section 3.3: Prove Lines are Parallel
Converse: switching the hypothesis and conclusion of an if-then statement.
Not all converses are true
Example of a Converse:
Original statement:
If there is a thunderstorm, then there are clouds in the sky.
Converse:

4. Section 3.3: Prove Lines are Parallel
Find the converse of the following statements:
If two angles are right angles, then they are congruent.
If Bob attends OVHS, then he has an OVHS student ID.
If a student is in 10th grade, then he has a laptop.

5. Section 3.3: Prove Lines are Parallel
The postulates and theorems learned in Section 3.4 all have true converses. Corresponding Angles Converse Postulate: If < 1 ≅ < 5, then line r is parallel to line s. 1 r 5 s

6. Section 3.3: Prove Lines are Parallel
Summary of other Converses: (all start by stating “If two lines are cut by a transversal so that…”
Alternate Interior Angles Converse: The alternate interior angles are congruent, then the lines are parallel
Alternate Exterior Angles Converse: The alternate exterior angles are congruent, then the lines are parallel
Same-Side Interior Angles Converse: The same-side interior angles are supplementary, then the lines are parallel

7. Section 3.3: Prove Lines are Parallel
Try together: Pg. 165 #10-15 (all)
Homework: Worksheet “Determine Which Lines are Parallel”