Question

In figure, ABCD, ABFE and CDEF are parallelograms. Prove that ar(ΔADE) = ar(ΔBCF).

Answer 1

Here, ABCD, CDEF and ABFE are parallelograms:

Which implies:

AD = BC

DE = CF and

AE = BF

Again, from triangles ADE and BCF:

AD = BC, DE = CF and AE = BF

By SSS criterion of congruence, we have

ΔADE ≅ ΔBCF

Since both the triangles are congruent, then ar(ΔADE) = ar(ΔBCF).

Hence Proved.