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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 ÐA and ÐB are a pair of interior angles on the same side of the transversal and ÐE and ÐF is the other such pair. Conclusion: a. ÐA + ÐB = 180°. b. ÐE + ÐF = 180° Proof: ÐA and ÐH form a linear pair, Therefore, ÐA + ÐH = 180° But ÐH = ÐB (By the axiom of corresponding angles). Therefore, Putting ÐB in the place of ÐH, we get ÐA + ÐB = 180° Similarly we can also show thatÐ E + ÐF = 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.

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