Question

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

Explanation:

Step1: Identify Right Angles

Both $\angle Y$ and $\angle N$ are right angles ($90^\circ$), so $\angle Y \cong \angle N$.

Step2: Identify Vertical Angles

$\angle XZY$ and $\angle MZN$ are vertical angles, so $\angle XZY \cong \angle MZN$.

Step3: Apply AA Similarity

By the Angle - Angle (AA) Similarity Criterion, if two angles of one triangle are congruent to two angles of another triangle, the triangles are similar. Since $\angle Y \cong \angle N$ and $\angle XZY \cong \angle MZN$, $\triangle XYZ \sim \triangle MNZ$.

Answer:

Similar: $\triangle XYZ \sim \triangle MNZ$ by the AA (Angle - Angle) Similarity Criterion.