S and T are points on sides PR and QR of ∆PQR such that ∠P = ∠RT – InterviewSolution

InterviewSolution

1.

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

Answer»

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.

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