Question

prove that : if a transversal intersects two lines such that the pair of alternate interior angles are equal , then the two lines are parallel

Answer 1

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Answer 2

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____________

Given: -

A transversal AB intersects two lines PQ and RS such that

∠PLM = ∠SML

To Prove: PQ ||RS

Use 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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