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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.
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Solution
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 ( 
(ii) and AX || YC
(iii) AXCY is a parallelogram (A pair of opposite sides are equal and parallel)
Hence proved.
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