If in two triangles ABC and PQR, $\frac{AB}{QR} = \frac{BC}{PR} = \frac{CA}{PQ}$, then which of the following is correct?
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Question

If in two triangles ABC and PQR, $\frac{AB}{QR} = \frac{BC}{PR} = \frac{CA}{PQ}$, then which of the following is correct?

Accepted Answer

The correct option is $	riangle PQR \sim 	riangle CAB$. According to the given condition of similarity based on side-side-side (SSS) criterion, the corresponding vertices must be matched properly. Here, the ratio of sides is $AB/QR = BC/PR = CA/PQ$. This means side AB corresponds to QR, BC corresponds to PR, and CA corresponds to PQ. Therefore, vertex A corresponds to Q, vertex B corresponds to R, and vertex C corresponds to P. Thus, $	riangle ABC$ is similar to $	riangle QRP$, which can also be written in cyclic order or rearranged accordingly. Checking the given options, $	riangle PQR \sim 	riangle CAB$ is mathematically consistent with the vertex correspondence.

Triangles

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