Question

If the bisector of a pair of alternate interior angle are parallel prove that given lines are parallel

Answer 1

Given:

Here, as shown in the figure given below let AC be the bisector of ∠PAB and BD be the bisector of ∠ABS.

∴ ∠PAC = ∠CAB = x

∠ABD = ∠DBS = y

It is also given that AC║BD

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

∴ x = y

⇒ 2x = 2y    [ Multipying both the sides with 2 ]

⇒ ∠PAB = ∠ABS

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

Hence proved.