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

## Solution :

Given : $$\triangle$$ RPQ and $$\triangle$$ RTS where $$\angle$$ P = $$\angle$$ RTS

To prove : $$\triangle$$ RPQ ~ $$\triangle$$ RTS

Proof : In $$\triangle$$ RPQ and $$\triangle$$ RTS

Given,    $$\angle$$ P = $$\angle$$ RTS

$$\angle$$ R = $$\angle$$ R                (common)

Hence, By AA similarity, $$\triangle$$ RPQ ~ $$\triangle$$ RTS