Question: Is $\triangle VWX \sim \triangle YZX$? Explain why or why not. The triangles are choose your answer... , $\angle XWV$ is choose your answer... to $\angle XZY$ because they are choose your answer... , and $\angle VXW$ is choose your answer... to $\angle YXZ$ because they are choose your answer... . Therefore, choose your answer... the corresponding angles are congruent, and the triangles are choose your answer... .

1. **State the problem:** Determine if $\triangle VWX$ is similar to $\triangle YZX$ and explain why or why not. 2. **Identify given information:** The diagram shows two horizontal parallel lines with points $Z$ and $Y$ on the top line and points $V$ and $W$ on the bottom line. Segments $ZW$ and $VY$ intersect at point $X$, forming two triangles. 3. **Recall similarity criteria:** Triangles are similar if their corresponding angles are congruent and their corresponding sides are proportional. 4. **Analyze angles:** Since the lines are parallel, alternate interior angles are congruent. - $\angle XWV$ corresponds to $\angle XZY$ because they are alternate interior angles formed by transversal $XW$ crossing parallel lines. - $\angle VXW$ corresponds to $\angle YXZ$ because they are alternate interior angles formed by transversal $XV$ crossing parallel lines. 5. **Conclusion:** Since two pairs of corresponding angles are congruent, by the Angle-Angle (AA) similarity criterion, the triangles $\triangle VWX$ and $\triangle YZX$ are similar. **Final answer:** The triangles are similar, $\angle XWV$ is congruent to $\angle XZY$ because they are alternate interior angles, and $\angle VXW$ is congruent to $\angle YXZ$ because they are alternate interior angles. Therefore, since the corresponding angles are congruent, the triangles are similar.