Data : ABCD, DCEF and ABFE are Parallelograms.
To Prove: ar.(∆ADE) = ar.(∆BCF)
Proof: In ABCD,
∴ AD = BC (Opposite sides of ) ………… (i)
Similarly, in DCFE, DE = CF (Opposite sides of ) ………..(ii)
Similarly, in ABFE, AE = BF (Opposite sides of ) ………… (iii)
In ∆ADE and ∆BCF, AD = BC ……… (1)
DE = CF ……… (2)
AE = BF ……… (3)
∴ ∆ADE ≅ ∆BCF (SSS postulate)
∴ ar.(∆ADE) = ar.(∆BCF).