ABCD is a parallelogram and X,Y are the mid points of sides AB and DC respectively . show that quadrlaterals AXCY is a parallelogram

given: ABCD is a llgm.

X & Y are the mid points of sides AB & DC respectively.

to prove: quadrilateral AXCY is a llgm.

proof: In AXCY,

AX = CY (AB = CD, X & Y are mid points)

AX ll CY (AB ll CD)

AXCY is a llgm. (if a pair of opp. sides of a quadrilateral are equal and parallel, then it is a llgm)

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