Question

Question 3
In the following figure, ABCD, DCFE and ABFE are parallelograms. Show that ar (ADE) = ar (BCF).

Answer 1

It is given that ABCD is a parallelogram. We know that opposite sides of a parallelogram are equal.
$\therefore AD=BC...\left(1\right)$
Similarly, for parallelograms DCEF and ABFE, it can be proved that,
DE = CF ...(2)
And, EA = FB ... (3)
In $\Delta ADEand\Delta BCF$,
AD = BC [Using equation (1)]
DE = CF [Using equation (2)]
EA = FB [Using equation (3)]
$\Rightarrow \Delta ADE\cong \Delta BCF$ (SSS congruence rule)
$\therefore Area\left(\Delta ADE\right)=Area\left(\Delta BCF\right)$