Question

S and T are points on sides PR and QR respectively of ∆PQR such that ∠P = ∠RTS prove that ∆RPQ~∆RTS.

Answer 1

Given: ∆PQR the points S and T on sides PR and QR such that ∠P = ∠RTS

To Prove: ∆RPQ~∆RTS

Proof: In ∆RPQ and ∆RTS

∠P = ∠RTS  [Given]

∠PRQ = ∠TRS [Common]

So, ∆RPQ~∆RTS [By AA similarity criterion]