Show that the line segment joining the mid-points of a pair of opposite sides of a parallelogram divides it into two equal parallelograms.

Let ABCD is a parallelogram. M and N are the

mid-points of AB and DC, respectively.

To prove ar (parallelogram AMND)=ar (parallelogram MBCN)

Proof Since, ABCD is a parallelogram.

∴ AB = DCan6 AB||DC

[by property of parallelogram]

=> AM = DN and AM||DN

[∵ M and N are the mid-points of AB and DC]

So, AMND is a parallelogram.

Similarly, we can prove that MBCN is also a parallelogram.

∴Parallelograms AMND and MBCN are on same base AB and between the same parallel lines AB and DC.

ar (parallelogram AMND) = ar (parallelogram MBCN)