Question

In \(\triangle ABC\) & \(\triangle PQR\), if \(AB = QR\), \(BC = PR\) and \(CA = PQ\), then :

• A. \(\triangle ABC \cong \triangle PQR\)
• B. \(\triangle CBA \cong \triangle PRQ\)
• C. \(\triangle BAC \cong \triangle RPQ\)
• D. \(\triangle PQR \cong \triangle BCA\)

Hint:

To quickly verify congruence options, check the corresponding segment pairs.
For option (B) \(\triangle CBA \cong \triangle PRQ\), the first two letters give segment \(CB\) corresponding to \(PR\).
The given data says \(BC = PR\), which matches.
The last two letters give \(BA\) corresponding to \(RQ\) (\(AB = QR\)), which also matches.
This systematic check helps avoid mistakes with vertex ordering.

Answer 1

The Correct Option is B

Step 1: Recall the SSS congruence idea.
When all three sides of one triangle equal the three sides of another, the triangles are congruent, but the order of the letters in the congruence statement must reflect exactly which vertex matches which.
Step 2: Match up vertices by looking at shared letters in the given equalities.
We are told $AB = QR$, $BC = PR$, $CA = PQ$. Vertex $A$ appears in $AB$ and $CA$, and vertex $Q$ appears in $QR$ and $PQ$, so $A$ and $Q$ play the same role. Vertex $B$ appears in $AB$ and $BC$, and vertex $R$ appears in $QR$ and $PR$, so $B$ and $R$ match. That leaves $C$ matching $P$.
Step 3: Build the congruence statement letter by letter.
Since $C \leftrightarrow P$, $B \leftrightarrow R$, $A \leftrightarrow Q$, writing the first triangle as $CBA$ forces the second to be written as $PRQ$ to keep the matching correct.
Step 4: Double check and conclude.
Reading off $\triangle CBA \cong \triangle PRQ$ gives $CB = PR$, $BA = RQ$, $CA = PQ$, all matching what was given, so this statement is the correct one. \[ \boxed{\triangle CBA \cong \triangle PRQ} \]