Question

m n y z x not similar or not necessarily similar similar: △xyz ~ △□ by the select

Explanation:

Step1: Identify Angles

$\angle MNY$ and $\angle XZY$ are right angles (so $\angle N = \angle Z = 90^\circ$). $\angle MYN$ and $\angle XYZ$ are vertical angles, so $\angle MYN = \angle XYZ$.

Step2: Determine Similarity Criterion

By AA (Angle - Angle) similarity criterion, if two angles of one triangle are equal to two angles of another triangle, the triangles are similar. So $\triangle XYZ \sim \triangle MNY$ (or $\triangle XYZ \sim \triangle MXN$ depending on labeling, but likely $\triangle MNY$) by AA similarity.

Answer:

$\triangle XYZ \sim \triangle MNY$ by the AA (Angle - Angle) Similarity Criterion (the first triangle should be $\triangle MNY$ or $\triangle MNM$ - correction: $\triangle XYZ \sim \triangle MNY$ with AA similarity).