Question

If in two triangles $△ABC$ and $△PQR$, $\frac{AB}{QR}=\frac{BC}{PR}=\frac{CA}{PQ}$, then

• A. $△PQR~△CAB$
• B. $△PQR~△ABC$
• C. $△CBA~△PQR$
• D. $△BCA~△PQR$

Answer 1

The correct option is A

$△PQR~△CAB$

Explanation for the correct option:

Determine the similarity:

Let us draw a suitable diagram.

It is given that, in two triangles $△ABC$ and $△PQR$,

$\frac{AB}{QR}=\frac{BC}{PR}=\frac{CA}{PQ}$

$\Rightarrow \frac{CA}{PQ}=\frac{AB}{QR}=\frac{BC}{PR}$

$\Rightarrow \frac{CA}{PQ}=\frac{AB}{QR}=\frac{BC}{RP}$

It means that the sides of $△PQR$ are in proportion with the sides of the $△CAB$.

The, using the SSS (Side-Side-Side) similarity criterion, it can be concluded that,

$△PQR~△CAB$

Hence, option (A) is the correct option.