Question

if a transversal intersects two parallel lines such that the bisectors of a pair of corresponding angle are parallel then prove that the two lines are parallel

Answer 1

Let l and m be two lines (non-parallel) and n is the transversal

Given AC||BD and AB is the transversal

⇒∠1 = ∠3   (Since corresponding angles are equal)

⇒ 2∠1 = 2∠3 [AC is bisector of ∠A and BD is bisector of ∠B]    

=>l || m [Since a pair of corresponding angles is equal then lines are parallel]

Answer 2

Angle B is congruent to angle A......
corresponding angle.
line mll to line l