Q. 54.2( 252 Votes )

# S and T are points on sides PR and QR of Δ PQR such that ∠P = ∠RTS. Show that Δ RPQ ~ Δ RTS

In ΔRPQ and ΔRST,

RTS = QPS (Given)

R = R (Common to both the triangles)
If two angles of two triangles are equal, third angle will also be equal. As the sum of interior angles of triangle is constant and is 180°

ΔRPQ ΔRTS (By AAA similarity)

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