In Fig. 15.86, ABC and BDE are two equilateral triangles such that D is the mid-point of BC. AE intersects BC in F. Prove that

(i) ar(Δ BDE) = ar(Δ ABC)

(ii) ar(Δ BDE) = ar(Δ BAE)

(iii) ar(Δ BFE) = ar(Δ AFD)

(iv) ar(Δ ABC) = ar(Δ BEC)

(v) ar(Δ FED) = ar(Δ AFC)

(vi) ar(Δ BFE) = 2ar(Δ EFD)