[3-3] Proving Lines Parallel Mr. Joshua Doudt Geometry (H) October 16, 2015 Pg

Objective To determine whether two lines are parallel

Lesson Vocabulary Flow Chart

Essential Understanding You used parallel lines to find congruent and supplementary relationships of special angles pairs. In this lesson, you will do the converse. You will use the congruent and supplementary relationships of the special angle pairs to prove line parallel.

Theorem 3-4 Converse of the Corresponding Angle Theorem

Problem 1 – Identifying Parallel Lines l m ab

Theorem 3-5 Converse of the Alternative Interior Angles Thm.

Theorem 3-6 Converse of the Same-Side Interior Angle Thm.

Theorem 3-7 Converse of the Alternate Exterior Angles Thm.

Definition The proof of converse of the alternate interior angles theorem looks different than any proof you have seen so far in this course. You know two forms of proof – paragraph and two- column. In a third form, called flow proof, arrows show the logical connections between the statements.

Proof Theorem 3-5

Flow Chart for Theorem 3-5

Problem 2 – Writing Flow Proof of Theorem l m 5 Plan: Use pair of congruent vertical angles to relate either 1 or 7 to its corresponding angle.

Problem 3 Determine whether lines are parallel Line l and e are parallel to each other because of converse of corresponding angle theorem. j d l e

Problem 4 – Using Algbera

Joke Time What has 18 legs and catches flies? A baseball team. Who stole the soap? The robber ducky! What happened to the plant on the windowsill of the classroom? It grew square roots!

Homework Pg.160 #7-16