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

Explanation

In `/_\ADC`,
`S` is the mid-point of `AD` and `R` is the mid-point of `CD`
In `/_\ABC`,
`P` is the mid-point of `AB` and `Q` is the mid-point of `BC`.
Line segments joining the mid-points of two sides of a triangle is parallel to the third side and is half of of it.
`:.SR` parallel `AC` and `SR=1/2AC`.......................(1)
`∴PQ` parallel to `AC` and `PQ=1/2AC`.......................(2)
From (1) and (2), we get
`⇒PQ=SR` and `PQ` parallel to `SR`
So, In `PQRS`, one pair of opposite sides is parallel and equal.
Hence, `PQRS` is a parallelogram.
`PR` and `SQ` are diagonals of parallelogram `PQRS`.
So, `OP=OR` and `OQ=OS` since diagonals of a parallelogram bisect each other.
Hence proved.