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? \

$$\begin{tabular}{|l|l|} \\hline statement & reason \\\\ \\hline 1. $\\overline{ng} \\cong \\overline{jg}$ & 1. given \\\\ 2. $\\angle n$ and $\\angle j$ are right angles & 2. given \\\\ 3. $\\angle mgn \\cong \\angle kgj$ & 3. vert. $\\angle$s are $\\cong$ \\\\ 4. $\\angle n \\cong \\angle j$ & 4. rt. $\\angle$s are $\\cong$ \\\\ 5. $\\triangle mng \\cong \\triangle kjg$ & 5.? \\\\ \\hline \\end{tabular}$$

\bigcirc the reflexive property \bigcirc asa \bigcirc aas \bigcirc the third angle theorem

Explanation:

To determine the missing reason for proving \(\triangle MNG \cong \triangle KJG\), we analyze the given information:

• We have \(\overline{NG} \cong \overline{JG}\) (side),
• \(\angle N \cong \angle J\) (angle, right angles),
• \(\angle MGN \cong \angle KGJ\) (angle, vertical angles).

This matches the AAS (Angle - Angle - Side) congruence criterion, where two angles and a non - included side of one triangle are congruent to the corresponding two angles and non - included side of another triangle. The reflexive property is not relevant here (it applies to a side or angle being congruent to itself), ASA requires the side to be included between the two angles, and the third angle theorem is about finding a third angle, not proving congruence.

Answer:

C. AAS