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Geometry: Section 3.3 Proofs with Parallel Lines What you will learn: 1. Use the Corresponding Angles Converse 2. Construct parallel lines 3. Prove theorems about parallel lines 4. Use the Transitive Property of Parallel Lines Theorem 3.5 Corresponding Angles Converse If two lines are cut by a transversal so that corresponding angles are congruent ____________________________________, then the lines are parallel ____________________________________ Note: We just switched the hypothesis and conclusion of the Corresponding Angles Theorem, hence the converse. The converses of the Alternate Interior Angles Theorem, the Alternate Exterior Angles Theorem and the Consecutive Interior Angles Theorem are also true. 3 x 5 2 x 4 180 5 x 1 180 8 x 12 6 x 2 x 12 0 8 x 5 80 180 8 x 85 180 5 x 181 x 36.2 2 x 12 x6 8 x 95 x 11.875 Example: Construct a line parallel to the line m through point P using corresponding angles. P m 1) WZ bisects VWY, ZWY X 1) Given 2) VWZ ZWY 2) Def. of Bisects 3) VWZ X 3) Substitution ) WZ || XY ) Corr. Angles Converse Theorem 3.9 Transitive Property of Parallel Lines If two lines are both parallel to the same line, the lines are parallel to each other then _____________________________ If m || p and p || r, then m || r m p r HW: pp 142 – 144 / 3 – 9, 13 – 16, 21, 22, 25, 30, 34, 36