Question

Triangle D E F is reflected across D F to form triangle E G F. The lengths of sides E F and F G are congruent.
To prove that ΔDEF ≅ ΔDGF by SAS, what additional information is needed?

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

Answer 1

∠DFE ≅ ∠DFG.

Reason: DF is the axis of reflection, so ∠DFE = ∠DFG. With EF ≅ FG (given) and DF ≅ DF (common side), the two triangles are congruent by SAS.