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△ABC has ∠A = 50°, ∠B = 60°, BC = 6 cm. △PQR has ∠P = 60°, ∠Q = 70°, QR = 6 cm. Are they congruent?

Class 9SAS, ASA and AAS CongruenceGeometry — Triangles
  • AYes, by ASA
  • BNo — the equal sides are opposite different angles
  • CYes, by AAS
  • DYes, because all angles match

Step-by-Step Solution

∠C = 70° and ∠R = 50°, so B ↔ P, C ↔ Q, A ↔ R. BC corresponds to PQ, not QR. QR is opposite ∠P = 60°, while BC is opposite ∠A = 50°; the triangles have the same angles but different matching sides, so they are not congruent.
Answer: B) No — the equal sides are opposite different angles

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