Question

statements reasons

given: ec bisects ∠hgf
prove: △hge ≅ △fge

Explanation:

Step1: Identify given information

Given that \( \overline{GE} \) bisects \( \angle HGF \), so \( \angle HGE=\angle FGE \). Also, from the figure \( HG = FG \) (marked with the same cross - hatch) and \( GE=GE \) (common side).

Step2: Apply the SAS (Side - Angle - Side) congruence criterion

In \( \triangle HGE \) and \( \triangle FGE \):

• \( HG = FG \) (given, side)
• \( \angle HGE=\angle FGE \) (angle, from the angle - bisector)
• \( GE = GE \) (common side)

By the SAS congruence criterion, \( \triangle HGE\cong\triangle FGE \).

Answer:

\( \triangle HGE\cong\triangle FGE \) by the SAS (Side - Angle - Side) congruence criterion.