 Name: ___________________Date:___________________

 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 ÅA and ÅB are a pair of interior angles on the same side of the transversal and ÅE and ÅF is the other such pair. Conclusion: a. ÅA + ÅB = 180¯. b. ÅE + ÅF = 180¯ Proof: ÅA and ÅH form a linear pair, Therefore, ÅA + ÅH = 180¯ But ÅH = ÅB (By the axiom of corresponding angles). Therefore, Putting ÅB in the place of ÅH, we get ÅA + ÅB = 180¯ Similarly we can also show thatÅ E + ÅF = 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. Name: ___________________Date:___________________