Question

to prove that △def ≅ △dgf by sss, what additional information is needed? ∠def ≅ ∠dgf de ≅ dc dc ≅ gf ∠dfe ≅ ∠dfg

Explanation:

Step1: Recall SSS Congruence

SSS (Side - Side - Side) congruence states that if three sides of one triangle are congruent to three sides of another triangle, then the triangles are congruent.

Step2: Analyze the given triangles

In \(\triangle DEF\) and \(\triangle DGF\), we already know \(EF\cong GF\) (marked in the diagram) and \(DF = DF\) (common side).

Step3: Determine the missing side

For SSS, we need the third pair of sides. The sides \(DE\) and \(DC\) are the remaining sides. So, if \(\overline{DE}\cong\overline{DC}\), then by SSS \(\triangle DEF\cong\triangle DGF\).

Answer:

\(\overline{DE}\cong\overline{DC}\)