Question

complete the proof that \\( \triangle ghi \cong \triangle gji \\).

Explanation:

Step1: Reflexive property of congruence

Any segment is congruent to itself. So, $\overline{GI}\cong\overline{GI}$ by the reflexive property of congruence.

Step2: SSS (Side - Side - Side) congruence criterion

If three sides of one triangle are congruent to three sides of another triangle, then the two triangles are congruent.
We have $\overline{GJ}\cong\overline{GH}$ (given), $\overline{IJ}\cong\overline{HI}$ (given), and $\overline{GI}\cong\overline{GI}$ (reflexive property).
So, $\triangle GHI\cong\triangle GJI$ by the SSS (Side - Side - Side) congruence criterion.

Answer:

1. Reason: Reflexive property of congruence
2. Reason: SSS (Side - Side - Side) congruence criterion