Question

the proof that \\( \triangle mng \cong \triangle kjg \\) is shown.
given: \\( \angle n \\) and \\( \angle j \\) are right angles; \\( \overline{ng} \cong \overline{jg} \\)
prove: \\( \triangle mng \cong \triangle kjg \\)
what is the missing reason in the proof?

Explanation:

Step1: Recall triangle congruence theorems

We have two angles ($\angle N\cong\angle J$, $\angle MGN\cong\angle KGJ$) and a non - included side ($\overline{NG}\cong\overline{JG}$) that are congruent.

Step2: Match with the AAS theorem

The AAS (Angle - Angle - Side) theorem states that if two angles and a non - included side of one triangle are congruent to two angles and the corresponding non - included side of another triangle, then the two triangles are congruent.

Answer:

AAS