Chapter 14, Problem 3PE

To determine

To prove: $\Delta PSR\cong \Delta QRS$

Explanation of Solution

Given information:

  $\angle OSR\cong \angle ORS,\angle OPQ\cong \angle OQP$ of the given figure.

  

Calculation:

From $\Delta PSR$ and $\Delta QRS$ ,

  $\begin{array}{l}\angle PSO\cong \angle QRO,\angle OSR\cong \angle ORS\Rightarrow \angle PSR\cong \angle QRS\mathrm{................}(i)\\ SR=SR\text{ (Common side)}\\ PS=QR\text{ (Two congruent sides)}\end{array}$

Therefore by side-angle-side formula $\Delta PSR$ and $\Delta QRS$ are congruent. Which follows sides of congruent triamgles are equal that is $\text{PR=QS}$ .

Thus $\Delta PSR\cong \Delta QRS$ is proved.

Hence proved.