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### Middle/High School Algebra, Geometry, and Statistics (AGS)5.8 Parallel Lines - Interior Angles are Supplementary - I

 Theorem - III: If a transversal intersects a pair of parallel lines, then the interior angles on the same side of the transversal are supplementary. Hypothesis: l // m and a transversal 'p' intersects the two lines so that ĐA and ĐB are a pair of interior angles on the same side of the transversal and ĐE and ĐF is the other such pair. Conclusion: a. ĐA + ĐB = 180°. b. ĐE + ĐF = 180° Proof: ĐA and ĐH form a linear pair, Therefore, ĐA + ĐH = 180° But ĐH = ĐB (By the axiom of corresponding angles). Therefore, Putting ĐB in the place of ĐH, we get ĐA + ĐB = 180° Similarly we can also show thatĐ E + ĐF = 180°.,br> Note: According to the axiom-3 on corresponding angles, we know that if a transversal intersects two parallel lines, then the corresponding angles will be equal. Directions: Draw parallel lines and a transversal and show that the interior angles on the same side of the transversal are supplementary.