Question

If there are two triangles, $△$ABC and $△$PQR, such that, AB = QR, BC = PR and CA = PQ, then ___.

• A. $△$ABC $\cong$ $△$ PQR
• B. $△$CBA $\cong$ $△$ PRQ
• C. $△$ BAC $\cong$ $△$RPQ
• D. $△$PQR $\cong$ $△$ BCA

Answer 1

The correct option is B

$△$CBA $\cong$ $△$ PRQ

Among the given options, only for option '$△$CBA $\cong$ $△$PRQ' we will have the given conditions satisfied.

The conditions given are: AB = QR, BC = PR and CA = PQ.
For the option '$△$ABC $\cong$ $△$PQR' to be satisfied, $△$ABC must be congruent to $△$PQR, which can’t happen because AB = QR and not PQ.
For option '$△$BAC $\cong$ $△$RPQ' to be satisfied, $△$BAC must be congruent to $△$RPQ, which can’t happen because AB = QR and not PR.
For option '$△$PQR $\cong$ $△$BCA' to be satisfied, $△$PQR must be congruent to $△$BCA, which can’t happen because AB = QR and not RP.

Only option which has the correct symbolic representation with respect to the given information is $△$CBA $\cong$ $△$ PRQ.
So, $△$CBA$\cong$ $△$ PRQ by SSS congruence condition.