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CTET PAPER II 2021 · PYQ · Triangle Congruence · medium

In ΔABC and ΔDEF, if AB = EF, BC = DE and CA = FD, then

  1. A.ΔABC ≅ ΔDEF
  2. B.ΔABC ≅ ΔFED
  3. C.ΔABC ≅ ΔEFD✓ Correct
  4. D.ΔABC ≅ ΔDFE

Explanation

Matching corresponding sides: AB = EF means A↔E, B↔F. BC = DE means B↔E or D, C↔D or E. CA = FD means C↔F, A↔D. Pairing carefully: AB ↔ EF gives A→E, B→F; CA ↔ FD gives C→F, A→D — contradiction. Try: A↔E, B↔F, C↔D, then AB=EF ✓, BC=FD ✗ (should be DE). Try A↔F, B↔E, C↔D: AB=FE ✓, BC=ED ✓, CA=DF ✓. So ABC ≅ FED. Hmm, that's option (2). Let me recheck: AB = EF and writing F↔A and E↔B keeps AB=EF. So ABC ≅ FED. The correct correspondence gives ABC ≅ FED, option (2).
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