Question

to prove that △def ≅ △dgf by sas, what additional information is needed?
∠def ≅ ∠ dgf
∠dfe ≅ ∠ dfg
(overline{de}congoverline{dg})
(overline{dg}congoverline{gf})

Explanation:

Step1: Recall SAS criterion

SAS (Side - Angle - Side) congruence criterion states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent. In \(\triangle DEF\) and \(\triangle DGF\), we already have a common side \(\overline{DF}\). The included angle for the sides we need to consider is \(\angle DFE\) and \(\angle DFG\) which are already equal (from the figure's markings). We need the other pair of sides adjacent to the common angle to be congruent.

Step2: Identify the required side - congruence

The sides adjacent to \(\angle DFE\) and \(\angle DFG\) are \(\overline{DE}\) and \(\overline{DG}\) respectively. For \(\triangle DEF\cong\triangle DGF\) by SAS, we need \(\overline{DE}\cong\overline{DG}\).

Answer:

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