Question

Abcd is a Parellogram prove apb congruent to cod

Answer 1

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