complete the missing statements/reasons in the proof. given: $\overline{wz} \parallel \overline{xy}$; $\angle wxy \cong \angle yzw$ prove: $\overline{wx} \cong \overline{yz}$ statements and reasons | statements | reasons | | $\overline{wz} \parallel \overline{xy}$ | given | | $\angle wxy \cong \angle yzw$ | given | | $\angle xwy \cong \angle zyw$ | 1. | | $\overline{wy} \cong \overline{wy}$ | reflexive property | | $\triangle wxy \cong \triangle yzw$ | aas postulate | | $\overline{wx} \cong \overline{yz}$ | 2. |

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# Explanation:
## Step1: Identify Reason for ∠XWY ≅ ∠ZYW
Since $ \overline{WZ} \parallel \overline{XY} $ and $ \overline{WY} $ is a transversal, the alternate interior angles theorem applies. So $ \angle XWY \cong \angle ZYW $ because alternate interior angles are congruent when two parallel lines are cut by a transversal.
## Step2: Identify Reason for $ \overline{WX} \cong \overline{YZ} $
In congruent triangles $ \triangle WXY \cong \triangle YZW $ (by AAS), corresponding parts of congruent triangles are congruent (CPCTC). So $ \overline{WX} \cong \overline{YZ} $ because of CPCTC.

# Answer:
1. Alternate Interior Angles Theorem
2. Corresponding Parts of Congruent Triangles are Congruent (CPCTC)

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Explanation:

Step1: Identify Reason for ∠XWY ≅ ∠ZYW

Step2: Identify Reason for \( \overline{WX} \cong \overline{YZ} \)

Answer: