Question

period ____ date ____
gruent. if yes, state the reason you know them to beence statement. if not, circle no.
2)

can the triangles be proven congruent?
yes no
reason for congruence:
sss sas asa aas hl aaa ass
congruence statement: $\triangle abc\cong\triangle$ ______

Explanation:

Step1: Analyze the given information

We have two triangles \(\triangle ABC\) and \(\triangle MNC\). We know that \(\angle ACB=\angle MCN\) (vertically - opposite angles are equal). Also, we are given that \(AB = MN\) (marked as equal in the figure) and \(\angle B=\angle N\) (marked as equal in the figure).

Step2: Apply the AAS (Angle - Angle - Side) congruence criterion

The AAS congruence criterion states that if two angles and a non - included side of one triangle are equal to two angles and the corresponding non - included side of another triangle, then the two triangles are congruent.
In \(\triangle ABC\) and \(\triangle MNC\), \(\angle B=\angle N\), \(\angle ACB=\angle MCN\), and \(AB = MN\)

Answer:

YES; AAS; \(\triangle MNC\)