Chapter 9.3, Problem 6PSA

To determine

To Show: That the ratios of sides $PR,RS$ and $RT,ST$ are equal. i.e., $\frac{PR}{RS}\text{ =}\frac{RT}{ST}$

Explanation of Solution

Given information :

There are a tringle $PRS.$

  $RT$ is an altitude on the line $PS$ .

  

From the figure, $\angle PRT={90}^{\text{o}}$

Formula used :

Ratios of the sides in two similar triangles are equal to each other.

Proof :

From $\Delta PR\mathrm{T}\text{and }\Delta PRS$ ,

  $\begin{array}{l}\angle PTR=\angle RTS=90°\\ RT=RT\text{, common side}\\ \angle TSR\text{=}\angle TPR\end{array}$

So, both triangles are similar. Then,

  $\therefore \frac{PR}{RS}=\frac{RT}{ST}$ (Proved)