Question

gi bisects ∠hij and ∠hgj. complete the proof that △gij ≅ △gih.

Explanation:

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

The ASA criterion 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

We have \(\angle GIH\cong\angle GIJ\) (from step 3), \(\overline{GI}\cong\overline{GI}\) (from step 5), and \(\angle HGI\cong\angle IGJ\) (from step 4). The side \(\overline{GI}\) is the included side between \(\angle GIH\) and \(\angle HGI\) in \(\triangle GIH\), and between \(\angle GIJ\) and \(\angle IGJ\) in \(\triangle GIJ\)

Answer:

ASA (Angle - Side - Angle) Congruence Criterion.