Question

S and T are points on sides PR and QR of ΔPQR such that \(\angle\)P = \(\angle\)RTS. Show that ΔRPQ ~ ΔRTS.

Answer 1

Given: In ΔPQR, S and T are points on sides PR and QR

To Prove: ΔRPQ ~ ΔRTS

Proof: In ∆RPQ and ∆RST,
\(\angle\)RTS = \(\angle\)QPS (Given)
\(\angle\)R = \(\angle\)R (Common angle)  
∴ ∆RPQ ∼ ∆RTS (By AA similarity criterion)

Hence Proved