Question:
In figure, ABCD, ABFE and CDEF are parallelograms. Prove that ar(ΔADE) = ar(ΔBCF).
Solution:
Given that
ABCD is parallelogram ⇒ AD = BC
CDEF is parallelogram ⇒ DE = CF
ABFE is parallelogram ⇒ AE = BF
Thus, in Δs ADF and BCF, we have
AD = BC, DE = CF and AE = BF
So, by SSS criterion of congruence, we have
ΔADE ≅ ΔBCF
ar(ΔADE) = ar(ΔBCF)