Question

AP and BQ are the bisectors of the two alternate interior angles formed by the intersection of a transversal t with parallel lines l and m (Figure). Show that AP || BQ.

Answer 1

Given In the figure l || m, AP and BQ are the bisectors of ∠EAB and ∠ABH, respectively.

To prove AP || BQ

Proof Since, l || m and t is transversal.

Therefore, ∠EAB = ∠ABH  ...[Alternate interior angles]

`1/2 ∠EAB = 1/2 ∠ABH`  ...[Dividing both sides by 2]

∠PAB = ∠ABQ  ...[AP and BQ are the bisectors of ∠EAB and ∠ABH]

Since, ∠PAB and ∠ABQ are alternate interior angles with two lines AP and BQ and transversal AB.

Hence, AP || BQ.