In Fig. 15.81, ABCD and CDEF are parallelograms. Prove that

Question

In Fig. 15.81, ABCD and CDEF are parallelograms. Prove that ar(&#x394; ADE) = ar(&#x394; BCF).

Philoid · Accepted Answer

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 BCF, 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)