Question

In the given figure, T and M are two points inside a parallelogram PQRS such that PT = MR and PT || MR. Then prove that RT || PM and RT = RM

Answer 1

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.