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