Chapter 8.3, Problem 12PSB

To determine

To prove : The similarity of $\Delta NRT$ with respect to $\Delta NSP$ .

Explanation of Solution

Given information : Here, we have given that $\overline{SP}$ is altitude to $\overline{NR}$ and $\overline{RT}$ is altitude to $\overline{NS}$ .

Proof: As, $\overline{SP}$ is altitude to $\overline{NR}$ ,

  $\Rightarrow \angle SPN=90°$

Similarly, as $\overline{RT}$ is altitude to $\overline{NS}$ ,

  $\Rightarrow \angle RTN=90°$

  $\Rightarrow \angle RTN\cong \angle SPN$

Now, In $\Delta NRT$ and $\Delta NSP$

  $\angle RTN\cong \angle SPN$ (Proved above))

  $\angle N\cong \angle N$ (Common)

  $\Rightarrow \Delta NRT\sim \Delta NSP$ (By AA Similarity Rule)