Question

g is the incenter, or point of concurrency, of the angle bisectors of △ace. which statements must be true regarding the diagram? □ bg ≅ ag □ dg ≅ fg □ dg ≅ bg □ ge bisects ∠def □ ga bisects ∠baf

Explanation:

Step1: Recall in - center property

The in - center of a triangle is equidistant from the sides of the triangle. Since \(G\) is the in - center of \(\triangle ACE\), and \(DG\) and \(FG\) are the distances from \(G\) to the sides of \(\triangle ACE\), we have \(\overline{DG}\cong\overline{FG}\). There is no information to suggest that \(\overline{BG}\cong\overline{AG}\), \(\overline{DG}\cong\overline{BG}\), \(\overline{GE}\) bisects \(\angle DEF\) or \(\overline{GA}\) bisects \(\angle BAF\) based on the fact that \(G\) is the in - center of \(\triangle ACE\).

Answer:

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