Question: User: FIND THE ERROR Sean and Daniela are determining which lines are parallel in the figure below. Sean says that because $\angle 1 \cong \angle 2$, $WY \parallel XZ$. Daniela disagrees and says that because $\angle 1 \cong \angle 2$, $WX \parallel YZ$. Is either of them correct? Explain your reasoning.

1. **State the problem:** Sean and Daniela observe a quadrilateral $WXYZ$ with diagonal $WZ$. They note that $\angle 1$ at vertex $W$ and $\angle 2$ at vertex $Z$ are congruent. Sean claims $WY \parallel XZ$ based on this, while Daniela claims $WX \parallel YZ$. We need to determine who is correct. 2. **Recall the parallel line angle rules:** - If two lines are parallel, alternate interior angles formed by a transversal are congruent. - Conversely, if alternate interior angles are congruent, the lines cut by the transversal are parallel. 3. **Analyze the figure and angles:** - $\angle 1$ is formed between $WX$ and diagonal $WZ$ at vertex $W$. - $\angle 2$ is formed between $YZ$ and diagonal $WZ$ at vertex $Z$. 4. **Check which pairs of lines could be parallel based on $\angle 1 \cong \angle 2$:** - If $\angle 1$ and $\angle 2$ are alternate interior angles, then the lines they lie between and the transversal must satisfy the alternate interior angle theorem. 5. **Identify the transversal:** - The diagonal $WZ$ acts as the transversal. 6. **Determine the pairs of lines cut by $WZ$:** - Lines $WX$ and $YZ$ are on opposite sides of $WZ$. - Lines $WY$ and $XZ$ are not on opposite sides of $WZ$ in a way that would make $\angle 1$ and $\angle 2$ alternate interior angles. 7. **Conclusion:** - Since $\angle 1$ and $\angle 2$ are congruent and are alternate interior angles formed by transversal $WZ$ intersecting lines $WX$ and $YZ$, the lines $WX$ and $YZ$ are parallel. - Therefore, Daniela is correct, and Sean is incorrect. **Final answer:** $$WX \parallel YZ$$