Question

△xyz was reflected to form △lmn.
which statements are true regarding the diagram? choose four correct answers.
$overline{xz}congoverline{ln}$
$angle zcongangle l$
$overline{yz}congoverline{ml}$
$\triangle xyzcong\triangle lmn$

Explanation:

Step1: Analyze triangle congruence

Since \(\triangle XYZ\) was reflected to form \(\triangle LMN\), the two triangles are congruent, so \(\triangle XYZ\cong\triangle LMN\).

Step2: Check side - angle congruence

By the property of congruent triangles, corresponding sides and angles are congruent.
For \(\overline{YZ}\) and \(\overline{ML}\), in congruent triangles \(\triangle XYZ\) and \(\triangle LMN\), \(Y\) corresponds to \(M\) and \(Z\) corresponds to \(L\), so \(\overline{YZ}\cong\overline{ML}\).
For \(\overline{XZ}\) and \(\overline{LN}\), \(X\) corresponds to \(L\) and \(Z\) corresponds to \(N\), so \(\overline{XZ}\cong\overline{LN}\).
For angles, \(\angle Z\) in \(\triangle XYZ\) and \(\angle N\) in \(\triangle LMN\) are corresponding angles (\(\angle Z\cong\angle N\)), not \(\angle Z\cong\angle L\).

Answer:

\(\overline{XZ}\cong\overline{LN}\), \(\overline{YZ}\cong\overline{ML}\), \(\triangle XYZ\cong\triangle LMN\) (assuming the fifth option which is correct based on congruence rules if it's a valid one related to the congruent triangle properties like \(\angle X\cong\angle L\) etc. But with the given options in the problem structure, the three correct ones from the presented options are \(\overline{XZ}\cong\overline{LN}\), \(\overline{YZ}\cong\overline{ML}\), \(\triangle XYZ\cong\triangle LMN\))