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In △ABC, ∠A = 40°, ∠B = 60°, AC = 5 cm. In △DEF, ∠D = 40°, ∠F = 80°, DF = 5 cm. Are they congruent?

Class 9SAS, ASA and AAS CongruenceGeometry — Triangles
  • AYes, by ASA: △ABC ≅ △DEF
  • BYes, but only by AAA
  • CNo, the angles are different
  • DCannot be decided

Step-by-Step Solution

∠C = 180° − 40° − 60° = 80° = ∠F. Now ∠A = ∠D, AC = DF and ∠C = ∠F, with AC between ∠A and ∠C: ASA.
Answer: A) Yes, by ASA: △ABC ≅ △DEF

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