Question

In Fig. ABCD and CDEF are parallelograms. 

Prove that ar(Δ ADE) = ar(Δ BCF).

Answer 1

Given that, 

ABCD is a parallelogram 

So, 

AD = BC 

CDEF is a parallelogram 

So, 

DE = CF 

ABFE is a parallelogram 

So, 

AE = BF 

Thus,

In ΔADE and ΔBCF, we have

AD = BC 

DE = CF 

And, 

AE = BF 

So, 

by SSS congruence rule, we have

 Δ ADE ≅ ΔBCF 

Therefore, 

Area (Δ ADE) = Area (Δ BCF)