Question

In the given Figure, $ABCD,DCFE$ and $ABFE$ are parallelograms. Show that $ar\left(ADE\right)=ar\left(BCF\right)$.

Answer 1

Since $ABCD$ is a parallelogram, therefore sides $AD$ and $BC$ are equal.

Since $DCFE$ is also a parallelogram, therefore, sides $DE$ and $FC$ are equal.

Since $ABFE$ is also a parallelogram, therefore, sides $AE$ and $BF$ are equal.

So, triangles $ADE$ and $BCF$ are congruent by $SSS$ congruency rule.

$\therefore$ Corresponding angles are equal in both triangles

So, the areas will be equal.

Therefore $ar\left(ADE\right)=ar\left(BCF\right)$.