Question

The straight line joining the mid-points of the opposite sides of a parallelogram divides it into two parallelograms of equal area.

• A. True
• B. False

Answer 1

The correct option is A True

Given : $ABCD$ is a parallelogram with $AB\parallel CD$ and $AD\parallel BC$.

Let $M$ and $N$ be the mid points of $AB$ and $DC$ respectively.

Then $AM=\frac{1}{2}AB$ and $DN=\frac{1}{2}DC$

But $AB=CD(ABCDisa\parallel gm)$

$\therefore AM=DN$ and $AM\parallel DN$

Thus $AMND$ is a parallelogram.

Similarly $MBCN$ is a parallelogram.

Then $AM=MB=DN=NC$

We know that parallelograms with equal base and between the same parallel lines are equal in area.

$\Rightarrow Ar(\parallel gmAMND)=Ar(\parallel gmMDCN)$