Question

A diagonal divides the parallelogram into two triangles of equal area.

• A. True
• B. False

Answer 1

The correct option is A

True

In parallelogram $ABCD,AC$ is the diagonal.

$DE$ and $BF$ are the perpendiculars from the vertices $D$ and $B$ respectively on $AC$.

The perpendiculars, $DE$ and $BF$ are equal, i.e., $DE=BF=h$

Now, area of $△ACD=\frac{1}{2}\times AC\times DE$

$=\frac{1}{2}\times AC\times h$ ... (i)

Area of $△ACB=\frac{1}{2}\times AC\times BF$

$=\frac{1}{2}\times AC\times h$ ... (ii)

Clearly, (i) $=$ (ii) i.e. Area of $△ACD=$ Area of $△ACB$

Hence, a diagonal divides the parallelogram into two triangles of equal area.