Chapter 13.9, Problem 3CE

To determine

To show: The side $\overline{OR}$ is perpendicular to the side $\overline{QS}$ .

Explanation of Solution

Given information:

The figure is shown below:

  

Proof:

As shown in figure, the quadrilateral $OQRS$ is a rectangle or square.

The length of the side $OQ$ is $a$ , side $QR$ is $a$ , side $SR$ is $a$ and side $OS$ is $a$ .

As the length of all the sides of quadrilateral are equal. So, the quadrilateral $OQRS$ is a square.

The sides $OR$ and $QS$ are the diagonals of the square. The diagonals of the square are always perpendicular to each other.

So, diagonal $OR$ and $QS$ are perpendicular to each other.

Hence, it is proved that $\overline{OR}\perp \overline{QS}$ .