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

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

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:

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.

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

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

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