Question

Show that the line segments joining the mid-points of the opposite sides of a quadrilateral bisect each other.

Answer 1

Let ABCD is a quadrilateral in which P, Q, R and S are midpoints of sides AB, BC, CD and DA respectively join PQ, QR, RS, SP and BD 

In ΔABD, S and P are the midpoints of AD and AB respectively. 

So, by using midpoint theorem we can say that

As in quadrilateral SPQR one pair of opposite side are equal and parallel to each other. 

So, SPQR is parallelogram 

Since, diagonals of a parallelogram bisect each other. 

Hence PR and QS bisect each other.