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Geometry 3.3 Big Idea: Prove Lines are Parallel The converses of the theorems we learned yesterday are true which leads to new theorems. (Remember, not all converses are true, but these are.) Postulate 16: Corresponding Angles Converse If two lines are cut by a transversal so that the corresponding angles are congruent, then the lines are parallel. Ðx @ Ðy L1 || L2 Alternate Interior Angles Converse: If two lines are cut by a transversal so that the alternate interior angles are congruent, then the lines are parallel. m || n Alternate Exterior Angles Converse: If two lines are cut by a transversal so that the alternate exterior angles are congruent, then the lines are parallel. a b Ð1@ Ð8 a || b Consecutive Interior Angles Converse: If two lines are cut by a transversal so that the consecutive interior angles are supplementary, then the lines are parallel. Ð4 +Ð6 =180 m || n Transitive Property of Parallel Lines If two lines are parallel to the same line, then they are parallel to each other. p q r If p || q and q || r, then p || r. Example: Find the value of x that m (3x + 5) makes m || n. n 65 Example: Is m || n? m 75 n 105
