Question

In Fig.,$\frac{QR}{QS}=\frac{QT}{PR}$ and $\angle 1=\angle 2$. Show that $△PQS\sim △TQR$.

Answer 1

In $△PQR$,
Since, $\angle 1=\angle 2$
$\therefore$ $PR=PQ$ (Opposite sides of equal angles are equal) $.....\left(1\right)$
In $△PQS$ and $△TQR$,
$\frac{QR}{QS}=\frac{QT}{PR}....\left(Given\right)$
i.e., $\frac{QR}{QS}=\frac{QT}{PQ}....\left(From1\right)$
Also, $\angle Q$ is common
$\therefore$ By SAS criterion of similarity, $△PQS\sim △TQR.$