△ ABC and △ RPQ are congruent, then the side of △ ABC that corresponds to PQ is:

Correct — A. A congruence statement is read letter by letter, in the order written.

△ABC ≅ △RPQ pairs A ↔ R, B ↔ P, C ↔ Q.

PQ joins the second and third letters of RPQ.
The second and third letters of ABC are B and C.

So PQ corresponds to BC — option (a).

Why the others are wrong

• (b)
  AR — AR is not a side of either triangle. A is a vertex of △ABC and R a vertex of △RPQ, so the segment joining them belongs to neither.
• (c)
  CA — CA joins the third and first letters of ABC, which map to Q and R. CA therefore corresponds to QR, not to PQ.
• (d)
  AB — AB joins the first and second letters of ABC, which map to R and P. AB therefore corresponds to RP, not to PQ.

A congruence statement is an ordered claim. Writing △ABC ≅ △RPQ asserts A = R, B = P and C = Q as matching vertices, and every side and angle pairing follows from that order.

The trap is that the second triangle's letters are not in alphabetical order. RPQ breaks the reflex of matching R to A, and a candidate who matches alphabetically pairs P with A.

Corresponding sides are equal in length and corresponding angles equal in measure, which is what CPCT states.

Key facts

• In △ABC ≅ △RPQ the vertex pairing is A ↔ R, B ↔ P, C ↔ Q.
• PQ corresponds to BC, QR corresponds to CA, and RP corresponds to AB.
• CPCT: corresponding parts of congruent triangles are equal.

Common traps

• Matching the letters alphabetically instead of positionally.
• Picking AR, which takes one vertex from each triangle.
• Assuming the two triangles must be drawn the same way up for the pairing to hold.

No directly related past PYQ was found.