Question

prove that - If a transversal. intersects two lines such that a pair of alternate interior angles are equal, then the two lines are parallel.

Answer 1

here is ur answer dear.......

Answer 2

Answer:

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 alternate angles are equal, then the two lines are parallel to each other.

Hence, PQ║RS Proved.