Question

In parallelogram ABCD, X and Y are midpoints of opposite sides AB and DC respectively. Prove that:

(i) AX = YC
(ii) AX is parallel to YC
(iii) AXCY is a parallelogram.

Answer 1

Given: In parallelogram ABCD, X and Y are the mid-points of sides AB and DC respectively AY and CX are joined.

To prove :
(i) AX = YC
(ii) AX is parallel to YC
(iii) AXCY is a parallelogram

Proof: AB || DC and X and Y are the mid-points of the sides AB and DC respectively

(i) AX = YC (  of opposite sides of a parallelogram)

(ii) and AX || YC

(iii) AXCY is a parallelogram (A pair of opposite sides are equal and parallel)

Hence proved.