Chapter 5.5, Problem 3PSA

To determine

To show: $\Delta ROS\text{ is isosceles}$ .

Explanation of Solution

Given information:

Rectangle MPRS, $\overline{MO}\cong \overline{PO}$ .

  

Calculation:

MPRS is a rectangle.

  

  $\begin{array}{l}\text{In above figure,}\\ \text{MPRS is a reactangle}\text{. }\\ \overline{SM}\cong \overline{RP}\left\{\text{Opposite sides of a rectangles are equal}\right\}\\ \overline{MO}\cong \overline{PO}\left\{\text{Given}\right\}\\ {\left(\overline{SM}\right)}^2+{\left(\overline{MO}\right)}^2={\left(\overline{RP}\right)}^2+{\left(\overline{PO}\right)}^2\\ \Rightarrow {\left(\overline{SO}\right)}^2={\left(\overline{RO}\right)}^2\\ \Rightarrow \overline{SO}=\overline{RO}\\ \Rightarrow \Delta ROS\text{ is an isosceles triangle}\text{. }\end{array}$