In the given figure, $\frac{QR}{QS} = \frac{QT}{PR}$ and $\angle 1 = \angle 2$. Show that $ riangle PQS \sim riangle TQR$.

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Question

In the given figure, $\frac{QR}{QS} = \frac{QT}{PR}$ and $\angle 1 = \angle 2$. Show that $	riangle PQS \sim 	riangle TQR$.

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Accepted Answer

Step 1: In $	riangle PQR$, $\angle 1 = \angle 2 \Rightarrow PR = PQ$ (sides opposite equal angles)
Step 2: Given $\frac{QR}{QS} = \frac{QT}{PR} = \frac{QT}{PQ}$ (since $PR = PQ$)
Step 3: Also, $\angle Q = \angle Q$ (common angle)
Step 4: $	herefore 	riangle PQS \sim 	riangle TQR$ (SAS similarity)

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