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

Explanation

let PQRS is a quadrilateral and A,B,C,D are mid points of PQ,QR,RS,SP respectively

join all mid points we get a quadrilateral ABCD
since line joining mid points of PQ and
`AB||QS`similarly ,
`CD||QS`and so `AB||CD`
similarly `AD||BC`
so ABCD is a parallelogram

now diagonals of a parallelogram bisects each other so here PR and QS bisect each other.