Question

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

• A. ABC PQR
• B. CBA PRQ
• C. BAC RPQ
• D. PQR BCA

Answer 1

The correct option is B

CBA PRQ

Among the given options, only for option $B$ has the given conditions satisfied.
The conditions already known to us are that $AB=QR,BC=PR$ and $CA=PQ$
For option $A$ to be satisfied, $△ABC$ must be congruent to $△PQR,$ which can’t happen because $AB=QR$ and not $PQ.$
For option $C$ to be satisfied, $△BAC$ must be congruent to $△RPQ,$ which can’t happen because $AB=QR$ and not $PR.$
For option $D$ to be satisfied, $△PQR$ must be congruent to $△BCA,$ which can’t happen because $AB=QR$ and not $RP.$

Option $B$ has the perfect naming in all respects, so $△CBA\cong △PRQ$ by $SSS$ congruence condition.