Question

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

Answer 1

$\angle 1=\angle 2\Rightarrow PQ=PR$ (Property of Isosceles Triangle)

$Also,\frac{QR}{QS}=\frac{QT}{PR}$

$\Rightarrow \frac{QR}{QS}=\frac{QT}{PQ}$

$In\Delta PQSand\Delta TQR$

$\angle PQS=\angle TQR$ (common)

$\Delta PQS\sim \Delta TQR$........using SAS similarity criteria