From the image, the problem is to prove that $\triangle XYZ \cong \triangle ZWX$, using a two-column proof with statements and reasons. Let us work through the missing parts step by step.

Step 1: Review the provided information

1. Given: $\angle ZXY = \angle XZW$ (matching angles)
2. To Prove: $\triangle XYZ \cong \triangle ZWX$

We aim to use a congruence criterion like ASA (Angle-Side-Angle) or SAS (Side-Angle-Side) for proving congruence.

Complete the Table:

Row 2:

• Statement: $\angle XZY = \angle WZX$
  Reason: Vertical angles are congruent (the two triangles share this pair of angles).

Row 3:

• Statement: $XZ = XZ$
  Reason: Reflexive property (a side shared by both triangles).

Row 4:

• Statement: $\triangle XYZ \cong \triangle ZWX$
  Reason: ASA congruence criterion (two angles and the included side are congruent).

Would you like more details on any of the steps?
Here are 5 related questions to deepen your understanding:

1. Why does the reflexive property work for shared sides in triangles?
2. How do vertical angles help establish congruence between triangles?
3. Can other congruence criteria (like SAS) work in this proof? Why or why not?
4. How do given congruent angles simplify proofs involving parallelograms?
5. What other methods can verify that two triangles in a diagram are congruent?

Tip: In geometry proofs, always look for shared sides, vertical angles, or given parallel relationships to establish congruence more quickly.