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) congruence 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 \(DF = DF\) (common side). We need to show that the other two pairs of corresponding sides are congruent.

Step2: Analyze the options

We are looking for a side - congruence statement. Options with angle - congruence (\(\angle DEF\cong\angle DGF\) and \(\angle DFE\cong\angle DFG\)) are not relevant for SSS. Among the side - congruence options, we need to have \(\overline{DE}\cong\overline{DG}\) to satisfy the SSS criterion as we already have the common side \(DF\) and if \(\overline{DE}\cong\overline{DG}\), we just need to consider the third - side pair which is already in the context of the SSS check for the two triangles.

Answer:

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