Question

A transversal intersects two parallel lines. Prove that the bisectors of any pair of corresponding angles so formed are parallel.

Answer 1

Given Two lines AB and CD are parallel and intersected by transversal t at P and Q, respectively. Also, EP and FQ are the bisectors of angles ∠APG and ∠CQP, respectively.

To prove: EP || FQ

Proof: Given, AB || CD

⇒ ∠APG = ∠CQP  ...[Corresponding angles]

⇒ `1/2 ∠APG = 1/2 ∠CQP`  ...[Dividing both sides by 2]

⇒ ∠EPG = ∠FQP  ...[∵ EP and FQ are the bisectors of ∠APG and ∠CQP, respectively]

As these, are the corresponding angles on the transversal line t.

∴ EP || FQ

Hence proved.