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Theorem 3ersal intersects two lines such that a pair of alternate interior angles are equal,then the two lines are parallel. |
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Answer» A transversal AB intersects two lines PQ and RS such that∠PLM = ∠SML To Prove: PQ ||RSUse same figure as in Theorem 2.Proof: ∠PLM = ∠SML ……………equation (i) (Given)∠SML = ∠RMB …………equation (ii) (vertically opposite angles)From equations (i) and (ii);∠PLM = ∠RMB But these are corresponding angles.We know that if a transversal intersects two lines such that a pair of corresponding angles is equal, then the two lines ate parallel to each other.Hence, PQ║RS Proved. |
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