Final answer:
To prove ΔABC ≅ ΔDEF by SAS, it is necessary to show that segment AC is congruent to segment FE, along with one pair of congruent included angles and one other pair of congruent sides. Therefore correct option is C
Step-by-step explanation:
The student is asking what additional information is required to prove that two triangles, ΔABC and ΔDEF, are congruent by the Side-Angle-Side (SAS) postulate.
The SAS postulate states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the triangles are congruent.
Given this, if segment BC is congruent to segment EF, and we already know an angle in ΔABC that is congruent to an angle in ΔDEF, then to complete the SAS congruence argument, we would need to show that the other side, which is segment AC, is congruent to segment FE. It would not be sufficient to show that segment AC is congruent to segment EF or that segment BC is congruent to segment FE, because these segments would not be the ones creating the needed pair of congruent included angles.
Therefore, we need segment AC ≅ segment FE for the SAS postulate to apply.