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

Explanation

Solution
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∥AC` and `SR= 1/2AC ` ....(1)
∴`PQ∥AC` and `PQ= 1/2AC` ....(2)
From (1) and (2)
⇒`PQ=SR` and `PQ∥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.