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 (overline{de}congoverline{dg}) (overline{dg}congoverline{gf})

Explanation:

Step1: Recall SSS congruence criterion

SSS (Side - Side - Side) states that if three sides of one triangle are congruent to three sides of another triangle, then the two triangles are congruent. In \(\triangle DEF\) and \(\triangle DGF\), we already have \(EF\cong GF\) (marked in the diagram) and \(DF\) is common to both triangles (\(DF = DF\) by the reflexive property).

Step2: Identify the missing side - congruence

We need the third - side pair to be congruent. The missing side - congruence is \(DE\cong DG\).

Answer:

C. \(\overline{DE}\cong\overline{DG}\)