Question

statements reasons
given: eg bisects ∠hgf
prove: △hge ≅ △fge

Explanation:

Step1: Identify equal sides

Since \(GH = GF\) (given as marked in the triangle).

Step2: Use angle - bisector property

Because \(GE\) bisects \(\angle HGF\), so \(\angle HGE=\angle FGE\).

Step3: Common side

\(GE = GE\) (common side for \(\triangle HGE\) and \(\triangle FGE\)).

Step4: Apply SAS congruence criterion

By the Side - Angle - Side (SAS) congruence criterion (\(GH = GF\), \(\angle HGE=\angle FGE\), \(GE = GE\)), we can conclude that \(\triangle HGE\cong\triangle FGE\).

Answer:

\(\triangle HGE\cong\triangle FGE\) (by SAS congruence criterion)