Chapter 15, Problem 24RP

To determine

To prove: that the one of the horizontal sides $RS$ is greater than vertical sides $RQ$ as shown in the given figure. i.e. $RS>RQ$

Answer to Problem 24RP

  $RS>RQ$ .

Explanation of Solution

Given:

A quadrilateral $PQRS$ in which $PQ>RS,\angle Q\cong \angle S$ .

  

Calculation:

According to the question, $PQRS$ is a quadrilateral. Now, joining the one diagonal so that a line is formed. So, a line $\overline{QS}$ is drawn.

  $\begin{array}{l}PQ>RS,\angle Q\cong \angle S\\ \Rightarrow \angle PSQ>\angle PQS\\ \Rightarrow \angle SQR>\angle QSR\\ \therefore RS>RQ\end{array}$

Thus, $RS>RQ$

Hence, it is proved that one of the horizontal sides $RS$ is greater than vertical sides $RQ$ .