Question

Devansh proved that ΔABC ∼ ΔPQR using SAS similarity criteria. If he found ∠C = ∠R, then which of the following was proved true?

Options

• `(AC)/(AB) = (PR)/(PQ)`

• `(BC)/(AC) = (PR)/(QR)`

• `(AC)/(BC) = (PR)/(PQ)`

• `(AC)/(BC) = (PR)/(QR)`

Answer 1

`bb((AC)/(BC) = (PR)/(QR))`

Explanation:

Given:

△ABC ∼ △PQR

∠C = ∠R

For SAS similarity using ∠C and ∠R, the sides forming these angles must be in the same ratio.

In △ABC, the sides forming ∠C are AC and BC.

In △PQR, the sides forming ∠R are PR and QR.

Therefore, `(AC)/(PR) = (BC)/(QR)`

Rearranging the terms:

`(AC)/(BC) = (PR)/(QR)`