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