If ∆ABC and ∆QPR are congruent triangles such that AB = 7 cm, AC = 8 cm, ∠B = 65° and ∠C = 75°, then which of the following is true?

Correct — B. The order of the letters is the correspondence.

∆ABC ≅ ∆QPR pairs A ↔ Q, B ↔ P, C ↔ R

Sides follow the pairs:
AB ↔ QP, so PQ = 7 cm
AC ↔ QR, so QR = 8 cm

Angles follow the pairs:
∠C ↔ ∠R, so ∠R = 75°
∠B ↔ ∠P = 65°, and ∠Q = ∠A = 180° − 65° − 75° = 40°

PQ = 7 cm and ∠R = 75° → option (b)

Why the others are wrong

• (a)
  AC = PR and ∠P = 65° — ∠P = 65° is right, but AC pairs with QR, not PR. PR is the partner of BC, which the stem never gives.
• (c)
  ∠Q = 40° and RQ = 7 cm — ∠Q = 40° is right, but RQ pairs with AC, so RQ = 8 cm. The 7 cm side is PQ, the partner of AB.
• (d)
  ∠R = 75° and PQ = 8 cm — ∠R = 75° is right, but PQ pairs with AB, so PQ = 7 cm. 8 cm is the length of AC and of its partner QR.

In a congruence statement the order of the letters is the correspondence. The first vertex of one triangle matches the first of the other, the second the second, the third the third.

So ∆ABC ≅ ∆QPR means A ↔ Q, B ↔ P, C ↔ R. A side is matched through both endpoints (AB ↔ QP), an angle through its vertex (∠B ↔ ∠P).

Alphabetical order in the second name counts for nothing — only position does.

Key facts

• ∆ABC ≅ ∆QPR pairs A with Q, B with P and C with R.
• Corresponding parts of congruent triangles are equal (CPCT).
• The angles of a triangle sum to 180°, so ∠A = ∠Q = 40° here.
• In any triangle the longer side lies opposite the larger angle.

Common traps

• Matching by alphabetical order (A with P) instead of by position (A with Q)
• Accepting an option because one of its two parts is true — each wrong option here has one correct half
• Matching a side by one endpoint only, which sends AC to PR instead of QR

No directly related past PYQ was found.