Chapter 8.3, Problem 3PSA

To determine

To prove : The similarity of $\Delta NWO$ with respect to $\Delta SWT$ .

Explanation of Solution

Given information : Here, we have given that NPRV is a parallelogram.

Proof: As, NPRV is a parallelogram,

  $\begin{array}{l}\Rightarrow \overline{NP}\parallel \overline{VR}\\ \Rightarrow NO\parallel TS\end{array}$

Now, as $NO\parallel TS$

  $\Rightarrow \angle ONW\cong WST$ and $\angle NOW\cong WTS$ (Alternate Interior Angles)

Now, In $\Delta NOW$ and $\Delta STW$

  $\angle ONW\cong \angle WST$ (Proved above)

  $\angle NOW\cong \angle WTS$ (Proved above)

  $\Rightarrow \Delta NOW\sim \Delta STW$ (By AA Similarity Rule)