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2015-12-05T13:48:47+05:30

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
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