Question

In the following figure, $\frac{QR}{QS}=\frac{QT}{PR}$ and $\angle 1 =\angle 2$

Show that ΔPQR∼ΔTQR

Answer 1

Given: $\frac{QR}{QS}=\frac{QT}{PR}$ and $\angle 1 =\angle 2$

To Prove: ΔPQR∼ΔTQR

Proof: In ∆PQR,
$\angle$PQR = $\angle$PRQ
∴ PQ = PR ………………(i)

Using (i) we obtain
$\frac{QR}{QS}=\frac{QT}{QP}$.............(ii)

In ΔPQS and ΔTQR,
$\frac{QR}{QS}=\frac{QT}{QP}$ [using (ii)]
$\angle$Q=$\angle$Q
∴ ΔPQS∼ΔTQR

Hence Proved