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

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.

56.6

step-by-step explanation:

the ratio of the perimeters is equal to the scale.

the ratio of the areas is equal to the square of the scale.

34 / 20 = k

a / 19.6 = k²

substituting:

a / 19.6 = (34 / 20)²

a = 19.6 (34 / 20)²

a ≈ 56.6