Question

1 ( h ) is the midpoint of ( overline{g i} ) given
2 ( overline{i k} cong overline{i j} ) given
3 ( overline{h k} cong overline{g j} ) given
4 ( overline{g h} cong overline{h i} ) definition of midpoint
5

Explanation:

Step1: Recall the Side - Side - Side (SSS) Congruence Theorem

The SSS Congruence Theorem states that if three sides of one triangle are congruent to three sides of another triangle, then the two triangles are congruent.

Step2: Identify the triangles and their sides

We have two triangles \(\triangle GHJ\) and \(\triangle IHK\).
We know that \(\overline{GH}\cong\overline{HI}\) (from the definition of mid - point, statement 4), \(\overline{HJ}\cong\overline{IK}\) (statement 2), and \(\overline{HK}\cong\overline{GJ}\) (statement 3).

Answer:

Statement: \(\triangle GHJ\cong\triangle IHK\); Reason: SSS Congruence Theorem.