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. Show that AP is parallel to BQ.

Answer 1

Answer:

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.