Question

i is the midpoint of \\( \overline { g h } \\). complete the proof that \\( \angle f i h \cong \angle f i g \\).

Explanation:

Step1: Use SSS Congruence Criterion

Since \( \overline{FG}\cong\overline{FH}\), \( \overline{GI}\cong\overline{HI}\), and \( \overline{FI}\cong\overline{FI}\), by the Side - Side - Side (SSS) congruence criterion, \( \triangle FIH\cong\triangle FIG\).

Step2: Use Corresponding Parts of Congruent Triangles

If \( \triangle FIH\cong\triangle FIG\), then their corresponding parts are congruent. So, \( \angle FIH\cong\angle FIG\) (Corresponding Parts of Congruent Triangles are Congruent - CPCTC).

Answer:

1. \( \triangle FIH\cong\triangle FIG\); SSS Congruence Criterion
2. \( \angle FIH\cong\angle FIG\); CPCTC