Question

$S$ and $T$ are point on sides $PR$ and $QR$ of $\Delta PQR$ such that $\angle P=\angle RTS$. Show that $\Delta RPQ~\Delta RTS$.

Answer 1

Step 1: Construction

Draw the figure.

Given : $S$ and $T$ are point on sides $PR$ and $QR$ of $\Delta PQR$

And $\angle P=\angle RTS$

Step 2: Prove that $\Delta RPQ~\Delta RTS$

In $\Delta RPQand\Delta RTS$,

$$\begin{gathered} \angle RTS=\angle QPS \\ \angle R=\angle R(Commonangle) \end{gathered}$$

By AA similarity criterion, $\Delta RPQ~\Delta RTS$

Hence Proved.