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### Middle/High School Algebra, Geometry, and Statistics (AGS)5.6 Parallel Lines - Interior Angles are Supplementary - II

 Theorem - V: If a transversal intersects two coplanar lines in such a way that a pair of interior angles on the same side of the transversal are supplementary, then the two lines are parallel. Hypothesis: 'l' and 'm' are two coplanar lines. 'p' is the transversal intersecting them. ÐA and ÐB are a pair of interior angles on the same side of the transversal such that, ÐA + ÐB = 180°. Conclusion: l // m. Proof: Let ÐC be an angle forming a linear pair with ÐA. Then ÐA + ÐC = 180°. But ÐA + B = 180°, given. Therefore, ÐA + ÐB = ÐA + ÐC. Therefore, ÐB = ÐC That is the corresponding angles are equal. So by axiom-4, 'l' and 'm' must be parallel lines. Therefore, l // m. Directions: Draw parallel lines and a transversal and show that the interior angles are supplementary.