Question

gj bisects ∠hgi and (overline{gi}congoverline{gh}). complete the proof that ( \triangle gijcong\triangle ghj).

Explanation:

Step1: Recall the SAS (Side - Angle - Side) congruence criterion

Two triangles are congruent if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle.

Step2: Identify the sides and angle for \(\triangle GIJ\) and \(\triangle GHJ\)

We know that \(\overline{GI}\cong\overline{GH}\) (given), \(\angle HGJ\cong\angle IGJ\) (from the definition of angle bisector as \(\overrightarrow{GJ}\) bisects \(\angle HGI\)), and \(\overline{GJ}\cong\overline{GJ}\) (reflexive property of congruence).

Answer:

\(\triangle GIJ\cong\triangle GHJ\) (by the SAS congruence criterion)