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we know that diagonal of a parallelogram bisect each other there fore AO is equal to OC and DO is equal to OB in parallelogram ABCD AC is the diagonal and O is the median of triangle divide it into two eqaul parts of equal triangles this implies in triangle ABC, oc is median there fore ar(AOC)is equal to ar (BOC) (1)

similarly in triangle CBD, OB is median ar(COB) is equal to ar(BOD) (2)

in trianle BAD, OD is median ar(BOD) is equal to ar(AOD) (3)

NOW from 1,2 and 3 we get ar(AOC)=ar(BOC)=ar(BOD)=ar(AOD) hence, prooved