Question

In the following figure, bisectors AP and BQ of the alternate interior angles are parallel, then show that l ||m.

Answer 1

Given, In the following figure AP || BQ, AP and BQ are the bisectors of alternate interior angles ∠CAB and ∠ABF.

To show l || m

Proof Since, AP || BQ and t is transversal, therefore ∠PAB = ∠ABQ  ...[Alternate interior angles]

⇒ 2∠PAB = 2∠ABQ  ...[Multiplying both sides by 2]

∠CAB = ∠ABF

So, alternate interior angles are equal.

We know that, if two alternate interior angles are equal, then lines are parallel.

Hence, l || m.