Question

cw: triangle congruence theorems
if not congruent, write none in both slots.

these triangles can be proven congruent by

Explanation:

Step1: Identify the congruent triangles

We have two triangles \(\triangle GFI\) and \(\triangle GHI\).

Step2: Check the congruence conditions

We know that \(GI = GI\) (common side). \(\angle FGI=\angle HGI\) (given as marked angles) and \(\angle GIF = \angle GIH\) (linear - pair angles, \(\angle GIF+\angle GIH = 180^{\circ}\) and they are supplementary, so if \(\angle GIF\) and \(\angle GIH\) are adjacent and form a linear pair, and we assume \(GI\) is a bisector in terms of angles and the linear - pair property, \(\angle GIF=\angle GIH = 90^{\circ}\)).
By the Angle - Side - Angle (ASA) congruence theorem.

Answer:

These triangles can be proven congruent by \(ASA\), \(\triangle GFI\cong\triangle GHI\)