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
$overline{xy}congoverline{lm}$
$overline{yz}congoverline{mn}$
$angle zcongangle n$
no additional information is required.
$overline{xz}congoverline{nm}$

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 two triangles are congruent.
In \(\triangle YXZ\) and \(\triangle MLN\), we already have two pairs of congruent angles (\(\angle Y\cong\angle M\) and \(\angle X\cong\angle L\)).

Step2: Identify the non - included side

For AAS, we need to have a non - included side congruent.
If \(\overline{YZ}\cong\overline{MN}\), then in \(\triangle YXZ\) and \(\triangle MLN\), we have \(\angle Y\cong\angle M\), \(\angle X\cong\angle L\) (two angles) and \(\overline{YZ}\cong\overline{MN}\) (non - included side).

Answer:

\(\overline{YZ}\cong\overline{MN}\)