6. Show that the line segments joining the mid-points of the opposite sides of a quadrilateral bisect each other.
Let ABCD be a quadrilateral and P, Q, R and S are the mid points of AB, BC, CD and DA respectively. Now, In ΔACD, R and S are the mid points of CD and DA respectively. , SR || AC. Similarly we can show that, PQ || AC, PS || BD and QR || BD , PQRS is parallelogram. PR and QS are the diagonals of the parallelogram PQRS. So, they will bisect each other.
