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In the given figure, $\frac{QR}{QS} = \frac{QT}{PR}$ and $\angle 1 = \angle 2$, show that $\Delta PQS \sim \Delta TQR$.
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In $\Delta PQR, \angle 1 = \angle 2 \implies PR = PQ$. $\therefore \frac{QR}{QS} = \frac{QT}{PR} \implies \frac{QR}{QS} = \frac{QT}{PQ}$. Also, $\angle 1 = \angle 1$. $\therefore \Delta PQS \sim \Delta TQR$.