1. The problem states that triangles $\triangle EFI$ and $\triangle HGI$ are congruent, written as $\triangle EFI \cong \triangle HGI$. 2. Congruent triangles have corresponding angles and sides that are equal. 3. The congruency statement matches vertices in order: $E \leftrightarrow H$, $F \leftrightarrow G$, and $I \leftrightarrow I$. 4. Therefore, angle $F$ in $\triangle EFI$ corresponds to angle $G$ in $\triangle HGI$. 5. So, $\angle F = \angle G$. 6. The other options $\angle I$, $\angle H$, or "not congruent to another angle" are incorrect for angle $F$. Final answer: $F = G$.