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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. ĐA and ĐB are a pair of interior angles on the same side of the transversal such that, ĐA + ĐB = 180°. Conclusion: l // m. Proof: Let ĐC be an angle forming a linear pair with ĐA. Then ĐA + ĐC = 180°. But ĐA + B = 180°, given. Therefore, ĐA + ĐB = ĐA + ĐC. Therefore, ĐB = ĐC 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.