Let's complete the proof shown in the image step by step. The goal is to prove that $\overline{XY} \cong \overline{XZ}$.

Given:

• $X$ is the midpoint of $\overline{WY}$,
• $\overline{WX} \cong \overline{XZ}$.

Proof:

This table completes the two-column proof.

Would you like more detailed explanations or have any questions on these steps? Here are some related questions to explore this further:

1. What is the definition of a midpoint in geometry?
2. How does the transitive property of equality work in geometry proofs?
3. Can you explain why $\overline{XY} \cong \overline{XZ}$ implies equal lengths?
4. What role do congruent segments play in geometric proofs?
5. How would this proof change if $X$ were not the midpoint?

Tip: Always double-check your reasoning and definitions, as they provide the foundation for all proofs!