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

Explanation

ABCD is a parallelogram

`therefore` AB=DC and AB||DC

`1/2AB=1/2DC` and AE||DE

Now, `AE=DF` and AE||DF

`therefore` quadrilateral ABCD is a parallelogram

Similarly, quadrilateral EBCF is also a parallelogram

Since, AEFD and EBCF are two parallelograms on the same base EF and between the same parallels, AD and BC

ar(AEFD)=ar(EBCF)