Question

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Answer 1

angle A = angle C [opposite angles of parallelogram]

= 1/2 angle A= 1/2 angle C = angle XAY = angle YCD..... eqn 1

,,, now, DC parallel to AB and CY is transversal.

= angle YCD= angle CYB .............. eqn 2 [alternate interior angles]

from eqn 1 and 2 we get..

angle XAB = angle CYB

but , these are corresponding angles formed of a parallelogram when AX and CY are Cut transversal AB.

:. AX parallel to CY..

proved..