Chapter 9, Problem 30CR

To determine

To prove: The given four-sided figure i.e. NPST is parallelogram

Explanation of Solution

Given information:

VRST is a parallelogram

V is midpoint of NT

R is the midpoint of PS

Formula used:

In parallelogram, both the pairs of opposite sides are parallel and equal

Proof :

Since given,

VRST is a parallelogram

V is midpoint of NT

R is the midpoint of PS

Therefore,

  $\begin{array}{l}VR\parallel TS\\ \therefore NP\parallel TS\mathrm{......}\left(i\right)\\ \text{Similarly},VT\parallel RS\\ \therefore NT\parallel PS\mathrm{.....}\left(ii\right)\end{array}$

Thus, NPST is a parallelogram

Hence proved