In Fig. 9.31, ABCD, DCFE and ABFE are parallelograms. Show that ar (ADE) = ar (BCF).

It is given that ABCD is a parallelogram. We know that opposite sides of a parallelogram are equal

AD = BC (i)

Similarly, for parallelograms DCEF and ABFE

DE = CF (ii)

And,

EA = FB (iii)

In ΔADE and ΔBCF,

AD = BC [Using equation (i)]

DE = CF [Using equation (ii)]

EA = FB [Using equation (iii)]

ΔADE BCF (SSS congruence rule)

Area (ΔADE) = Area (ΔBCF)