Question

9 is △vwx ~ △yzx? explain why or why not.

Explanation:

Step1: Identify Vertical Angles

$\angle VXW$ and $\angle YXZ$ are vertical angles, so $\angle VXW = \angle YXZ$.

Step2: Identify Alternate Interior Angles

Since $ZY \parallel VW$ (from the parallel lines in the diagram), $\angle ZYX$ and $\angle WVX$ are alternate interior angles, so $\angle ZYX = \angle WVX$.

Step3: Apply AA Similarity Criterion

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 $\angle VXW = \angle YXZ$ and $\angle ZYX = \angle WVX$, $\triangle VWX \sim \triangle YZX$.

Answer:

Yes, $\triangle VWX \sim \triangle YZX$ by the AA (Angle - Angle) similarity criterion. We have $\angle VXW=\angle YXZ$ (vertical angles) and $\angle ZYX = \angle WVX$ (alternate interior angles from parallel lines $ZY\parallel VW$), so two pairs of congruent angles satisfy the AA similarity condition.