∠A = ∠C (Opposite angles of parallelogram ABCD)
Therefore, 1/2 ∠A = 1/2 ∠C
i.e., ∠YAX = ∠YCX (1)
Also, ∠AYC + ∠YCX = 180º (Because YA || CX) (2)
Therefore, ∠AYC + ∠YAX = 180º [From (1) and (2)]
So, AX || CY (As interior angles on the same side of the transversal are supplementary)