Question

complete the proof that ( \triangle fgi cong \triangle fhi ).

Explanation:

Step1: Recall the ASA (Angle - Side - Angle) Congruence Criterion

ASA states that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent.

Step2: Identify the congruent parts in \(\triangle FGI\) and \(\triangle FHI\)

• We have \(\angle GFI\cong\angle HFI\) (given).
• \(\overline{FI}\cong\overline{FI}\) (reflexive property of congruence).
• \(\angle FIG\cong\angle FIH\) (all right angles are congruent).

Answer:

ASA (Angle - Side - Angle) Congruence Criterion.