Question

In Fig., AX and CY are respectively the bisectors of the opposite angles A and C of a parallelogram ABCD. Show that AX || CY.

Answer 1

∠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)