Question

ar(AOB)=ar(COD).prove tha abcd is a parallelogram

Answer 1

as Ar(AOB)=ar(COD),
triangle AOB = COD (they are congruent)
by CPCT rule, CD= AB ----------------(A)
DO = OB ------------1
AO = CO-------------2
one pair of opposite sides are equal.
now in triangles COB and DOA ,
DO = OB (from 1)
AO = CO(from 2)
so they are isoceles triangles.
the angles OBC and OCB are equal with ODA and OAD (angles opposite to  equal sides are equal from 1 and 2)

thus the triangles ODA AND COB are also congruent.
by CPCT rule,
CB = DA.--------------(B)
from A and B , we get 2 pairs of opposite sides equal.so as the opposite sides are equal it is a parallelogram.

hope it helps!!!!!