Q8 of 77 Page 15

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

ar(Δ ADE) = ar(Δ BCF).


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)


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