Question

i is the midpoint of \\( \overline{gh} \\). complete the proof that \\( \angle gfi \cong \angle hfi \\).

Explanation:

Step1: Use SAS (Side - Angle - Side) Congruence Criterion

We have \(\overline{GI}\cong\overline{HI}\) (from step 4), \(\angle FIG\cong\angle FIH\) (from step 3), and \(\overline{FI}\cong\overline{FI}\) (from step 5). By the SAS (Side - Angle - Side) congruence criterion, \(\triangle FIG\cong\triangle FIH\).

Step2: Use Corresponding Parts of Congruent Triangles are Congruent (CPCTC)

Since \(\triangle FIG\cong\triangle FIH\), then their corresponding angles \(\angle GFI\) and \(\angle HFI\) are congruent.

Answer:

1. \(\triangle FIG\cong\triangle FIH\); SAS (Side - Angle - Side) Congruence Criterion