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.