Question

statements reasons
given: ec bisects <hgf
prove: △hgc ≅ △fgc

Explanation:

Step1: Write the given information

Given: \( \overline{GC} \) bisects \( \angle HGF \), so \( \angle HGC=\angle FGC \). Also, \( \overline{HG}=\overline{FG} \) (marked in the figure), and \( \overline{GC}=\overline{GC} \) (common side).

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

In \( \triangle HGC \) and \( \triangle FGC \), we have:

• \( \overline{HG}=\overline{FG} \) (Side)
• \( \angle HGC=\angle FGC \) (Angle)
• \( \overline{GC}=\overline{GC} \) (Side)

By the SAS congruence criterion, \( \triangle HGC\cong\triangle FGC \).

Answer:

\( \triangle HGC\cong\triangle FGC \) (by SAS congruence criterion)