In Fig., QR/QS = QT/PR and ∠1 = ∠2. Show that ΔPQS ≅ ΔTQR.

In ΔPQR,
Since, ∠1 = ∠2
∴ PR = PQ (Opposite sides of equal angles are equal) (1)
In ΔPQS and ΔTQR,
QR/QS = QT/PR (Given)
i.e., QR/QS = QT/PQ (From 1)
Also, ∠Q is common
∴ By SAS criterion of similarity, ΔPQS ≅ ΔTQR.