Question

To prove that ΔDEF ≅ ΔDGF by SAS (Side-Angle-Side), what additional information is needed?

a. ∠DEF ≅ ∠DGF
b. ∠DFE ≅ ∠DFG
c. DE ≅ DG
d. ∠DEG ≅ ∠DFG

Answer 1

Additional information needed to prove triangle congruence by SAS is the congruency of angles ∠DFE and ∠DFG (option b). This completes the necessary two congruent sides and the included congruent angle to satisfy the SAS postulate.

Step-by-step explanation:

To prove that ∆DEF ≅ ∆DGF by SAS (Side-Angle-Side), additional information that is needed is option (b) ∠DFE ≅ ∠DFG. This is because the SAS postulate requires two sides in a triangle to be congruent and the angle included between those two sides to be congruent as well. Here, we already have DE=DF and EF is shared by both triangles. Therefore, the congruency of ∠DFE and ∠DFG would suffice to prove ∆DEF ≅ ∆DGF by the SAS postulate.