We have been given a parallelogram PQRS and T and M are two points inside it.
Given also that PT = MR and PT || MR. ----- (1)
Join RT and PM.
Now, in the quadrilateral PMRT, one pair of opposite sides are parallel and equal from (1)
Therefore, PMRT is a parallelogram.
By the properties of parallelogram, the other pair of opposite sides are too parallel and equal.
Hence, RT || PM and RT = PM.
