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Section 3.3 Prove Lines are Parallel Goal • Use angle relationships to prove that lines are parallel. In Geometry, we have several theorems that help us determine if lines are parallel. They are the true converses of the theorems we learned in the last section. Example 1: Determine which of the following pairs of angles, fit into the given categories. a. Corresponding angles b. Alternate interior c. Alternate exterior d. Consecutive interior POSTULATE 16 CORRESPONDING ANGLES CONVERSE If two lines are cut by a transversal so the corresponding angles are congruent, then the lines are parallel. Example 2: Is enough information given to conclude that BD║EG? Justify your conclusion. a. b. ● 110º D ● B ● E 110º ● G Example 3: Find the value of x that makes m║n. B E 64º 65º D G Checkpoint: Find the value of x that makes a║b. THEOREM 3.4 ALTERNATE INTERIOR ANGLES CONVERSE If two lines are cut by a transversal so the alternate interior angles are congruent, then the lines are parallel. Section 3.3 Prove Lines are Parallel THEOREM 3.5 ALTERNATE EXTERIOR ANGLES CONVERSE If two lines are cut by a transversal so the alternate exterior angles are congruent, then the lines are parallel. THEOREM 3.6 CONSECUTIVE INTERIOR ANGLES CONVERSE If two lines are cut by a transversal so the consecutive interior angles are supplementary, then the lines are parallel. Example 4: Find the value of x so that p║q. a. b. Checkpoint: Use the diagram at the right. a. Find the value of x that makes a || b. b. Find the value of y that makes a || c. Another way to determine if two lines are parallel is by the Transitive Property of Parallel Lines: THEOREM 3.7 TRANSITIVE PROPERTY OF PARALLEL LINES If p║q and q║r, then p║r. If two lines are parallel to the same line, then they are parallel to each other.