Since opposite angles are equal in a parallelogram . Therefore , in parallelogram ABCD , we have ∠A = ∠C ⇒ 1 / 2 ∠A = 1 / 2 ∠C ⇒ ∠1 = ∠2 ---- i) [∵ AX and CY are bisectors of ∠A and ∠C respectively] Now, AB | | DC and the transversal CY intersects them. ∴ ∠2 and ∠3 ---- ii) [∵ alternate interior angles are equal ] From (i) and (ii) , we have ∠1 and ∠3 Thus , transversal AB intersects AX and YC at A and Y such that ∠1 = ∠3 i.e. corresponding angles are equal . ∴ AX | | CY .