Maths · Relations, type of relations, equivalence relations
and DEF are two triangles, then to ensure that two triangles ABC and DEF are con
\( \triangle \mathrm{ABC} \) and \( \triangle \) DEF are two triangles, then to ensure that two triangles ABC and DEF are congruent, 3 conditions \( \operatorname{given} ; A B=D E, A C=D F, \angle A B C=\angle \) DEF are
- A. sufficient but not necessary
- B. necessary but not sufficient
- C. neither necessary nor sufficient
- D. both necessary and sufficient
Step-by-step solution
The given conditions (AB=DE, AC=DF, ∠ABC=∠DEF) are SSA (side-side-angle) conditions. For two triangles to be congruent, these conditions must hold under a given correspondence, so they are necessary. However, SSA is not a valid congruence criterion because it can lead to two possible triangles (ambiguous case), so it is not sufficient. Hence the conditions are necessary but not sufficient.
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