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★ Similarity of triangles should be expressed symbolically using correct correspondence of their vertices.
In ΔPQR,
∠1 = ∠2
∠PQR = ∠PRQ [GIVEN]
∴ PR = PQ ……………..…(1)
[Sides opposite to equal angles of a triangle are also equal]
Given:
QR/QS = QT/PR
QR/QS = QT/PQ
QS/QR = PQ/QT…... …(ii) [Taking reciprocals]
[From eq (i)]
In ΔPQS and ΔTQR,
QS/QR = PQ/QT [From eq (ii)]
∠PQS = ∠TQR [ common]
∴ ΔPQS ~ ΔTQR [By SAS similarity criterion]
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