Question

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

Answer 1

Data: S and T are points on sides PR and QR of ∆PQR such that 

∠P = ∠RTS. 

To Prove: ∆RPQ ~ ∆RTS. 

In ∆RPQ and ∆RTS, 

∠P = ∠RTS (Data) 

∠PRQ = ∠SRT (Common) 

∴ 3rd angle ∠PRQ = ∠SRT 

∴ These are equiangular angular triangles. 

∴ Here A.A.A. similarity criterion. 

∴ ∆RPQ ~ ∆RTS.