Chapter 9, Problem 30CUR

To determine

To prove: the angle $\angle S$ equal to $\angle Q$ .

Answer to Problem 30CUR

The angle $\angle S$ equal to $\angle Q$ .

Explanation of Solution

Given:

The triangles are shown below:

Ratio of sides is equal as $\frac{PR}{TR}=\frac{SR}{QR}$ .

Calculation:

Consider triangles $\Delta PRS$ and $\Delta TRQ$ ,

  $\begin{array}{l}\angle PRS=\angle TRQ\left(\text{Vertical opposite angle}\right)\\ \frac{PR}{TR}=\frac{SR}{QR}\left(\text{Given}\right)\\ \therefore \Delta PRS\sim \Delta TRQ\left(SAS\right)\end{array}$

Hence,

  $\angle S\cong \angle Q$

Thus, this proves the angle $\angle S$ equal to $\angle Q$ .