Chapter 6, Problem 7CR

Solution

To Prove: $\Delta STP$ is isosceles.

Given information: NPRS is a quadrilateral, with diagonals $\overline{SP}$ and $\overline{NR}$ intersecting at O. $\overline{TO}$ is perpendicular to the plane of quadrilateral NPRS is provided in the question which will help to find the solution.

Proof: In $\Delta TOS$ and $\Delta TOP$

  $\angle TOS=\angle TOP$ (right angle)

ST = TP (sides opposite to equal angles are equal)

Hence, we can say that

  $\Delta STP$ is isosceles.