Question

if two parallel lines are intersected by transversal line then show that the bisector of any pair ofA.i.a are parallel

Answer 1

Given ∠PAC = ∠CAB = x

∠ABD = ∠DBS = y

It is also given that AC||BD

⇒ ∠CAB = ∠ABD [Alternate angles are equal]

That is x = y

⇒�2x = 2y

⇒�∠PAB = ∠ABS

∴ PQ||RS [Since alternate angles are equal, lines are parallel]