Question

determine the additional piece of information needed to show that the two triangles are congruent by the asa postulate. a $\angle n\cong\angle a$ b $\angle n\cong\angle m$ c $\angle c\cong\angle m$

Explanation:

Step1: Recall ASA (Angle - Side - Angle) postulate

ASA postulate states that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent.
In \(\triangle ABC\) and \(\triangle MNO\), we already know that \(BC\cong NO\) (given by the tick marks).

Step2: Analyze each option

• Option a: If \(\angle N\cong\angle A\), we have one angle (\(\angle B\) in \(\triangle ABC\) and \(\angle O\) in \(\triangle MNO\)) and a side (\(BC = NO\)), but \(\angle N\) and \(\angle A\) are not in the correct position for ASA.
• Option b: \(\angle N\cong\angle M\) is not relevant as we need angles that can form the ASA structure with the given side.
• Option c: If \(\angle C\cong\angle M\), then in \(\triangle ABC\) and \(\triangle MNO\), we have \(\angle C\cong\angle M\), \(BC\cong NO\), and \(\angle B\cong\angle O\) (by ASA, since the side \(BC\) (or \(NO\)) is between \(\angle B\) and \(\angle C\) (or \(\angle O\) and \(\angle M\))).

Answer:

\(c\)