In the following figure. \(\frac{QR}{QS} = \frac{QT}{PR}\) and ∠1 – InterviewSolution

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1.

In the following figure. \(\frac{QR}{QS} = \frac{QT}{PR}\) and ∠1 = ∠2. Show that ∆PQS ~ ∆TQR.

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Data: Here \(\frac{QR}{QS} = \frac{QT}{PR}\) and ∠1 = ∠2

To prove: ∆PQS ~ ∆TQR.

In ∆PQS and ∆TQR, we have

\(\frac{QR}{QS} = \frac{QT}{PR}\)

∠PQR = ∠PRQ (∵ ∠1 = ∠2)

Here, Similarity criterion used here is side, angle, side (SAS).

∴ ∆PQS ~ ∆TQR.

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