Question

$\text{In parallelogram ABCD, X and Y are mid-points of opposite sides AB and DC respectively. Prove that :}\left(i\right)AX=YC\left(ii\right)AX\text{is parallel to YC}\left(iii\right)\text{AXCY is a parallelogram.}$

Answer 1

$\text{Given : In parallelogram ABCD, X and Y are the mid-points of sides AB and DC respectively AY an CX are joined}$

$\text{To Prove :}\left(i\right)AX=YC\left(ii\right)\text{AX is parallel to YC}\left(iii\right)\text{AXCY is a parallelogram}\text{Proof :}\because AB||DC\text{and X and Y are the mid-points of the sides AB and DC respectively}\left(i\right)\therefore AX=YC\left(\frac{1}{2}\text{of opposite sides of a parallelogram}\right)\left(ii\right)andAX||YC\left(iii\right)\because \text{AXCY is a parallelogram}\left(\text{A pair of opposite sides are equal and parallel}\right)\text{Hence Proved.}$