Question

If in two triangles DEF and PQR, ∠D = ∠Q and ∠R = ∠E, then which of the following is not true?

Options

• `(EF)/(PR) = (DF)/(PQ)`

• `(DE)/(PQ) = (EF)/(RP)`

• `(DE)/(QR) = (DF)/(PQ)`

• `(EF)/(RP) = (DE)/(QR)`

Answer 1

`(DE)/(PQ) = (EF)/(RP)`

Explanation:

Given, in ∆DEF and ∆PQR, ∠D = ∠Q, ∠R = ∠E

∴ ∆DEF ~ ∆QRP ......[By AAA similarity criterion]

⇒ ∠F = ∠P   .....[Corresponding angles of similar triangles]

∴ `(DE)/(QP) = (ED)/(RQ) = (FE)/(PR)`