Question

given the figure of triangles below with sides and angles as marked.
select the additional information that is required in order to know the triangles are congruent by angle angle side congruency.
$\bigcirc\\ \angle z\cong\angle n$
$\bigcirc\\ \overline{yz}\cong\overline{mn}$
$\bigcirc\\ \overline{xy}\cong\overline{lm}$
$\bigcirc\\ \overline{xz}\cong\overline{nm}$
$\bigcirc\\ $ no additional information is required.

Explanation:

Step1: Recall AAS congruence

Angle - Angle - Side (AAS) congruence 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 triangles are congruent.

Step2: Analyze the given angles

In \(\triangle YXZ\) and \(\triangle LMN\), we know that \(\angle Y\cong\angle M\) and \(\angle X\cong\angle L\) (given by the marked angles).

Step3: Check the non - included side

For AAS, we need a non - included side. The non - included side for \(\angle Y\) and \(\angle X\) in \(\triangle YXZ\) is \(XY\), and the non - included side for \(\angle M\) and \(\angle L\) in \(\triangle LMN\) is \(LM\). If \(\overline{XY}\cong\overline{LM}\), then by AAS, \(\triangle YXZ\cong\triangle LMN\)

Answer:

\(\overline{XY}\cong\overline{LM}\)