Question

Triangle DEF and triangle DGF are shown in the diagram.


To prove that ΔDEF ≅ ΔDGF by SSS, what additional information is needed?

∠DEF ≅ ∠DGF
∠DFE ≅ ∠DFG
DE ≅ DG
DG ≅ GF

Answer 1

DE ≅ DG.

Reason: SSS needs three pairs of equal sides. DF is common and EF ≅ GF is already given in the diagram, so the missing side equality is DE ≅ DG. (The angle congruences are irrelevant to an SSS proof, and DG ≅ GF does not give the needed equality of DE and DG.)