Question

. If a transversal intersects two lines such that the bisectors of a pair of corresponding
angles are parallel, then prove that the two lines are parallel.

Answer 1

I think this may help you and you can refer this

Answer 2

given: A transversal AB intersects two lines PQ and RS such that ∠ PLM = ∠ SMLTo prove: PQ || RSProof: ∠ PLM = ∠ SML (given) ....... (i)∠ SML = ∠ RMB ....... (ii) (vertically opposite angles)From equations (i) and (ii),∠ PLM = ∠ RMBAs these are corresponding angles and corresponding angles equal only if given lines PQ and RS are parallel.∴ PQ || RS