Question

two lines are intersected by a transversal in such a way that alternate angles are equal prove that lines are parallel

Answer 1

Solution: Given: - A transversal AB intersects two lines PQ and RS such that
∠PLM = ∠SML

To Prove: PQ ||RS
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.