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Check my work and give me the answers for the reasons

Let's go step by step through your proof to check your work and provide the correct answers.

### Given Information:
- **Given:** \( X \) is the midpoint of \( \overline{WY} \)
- **Prove:** \( \overline{XY} \cong \overline{XZ} \)

### Statement and Reason Columns:

#### Step 1:
- **Statement:** \( X \) is the midpoint of \( \overline{WY} \)
- **Reason:** **Given**

This is correct as it's directly given in the problem.

#### Step 2:
- **Statement:** \( WX = XY \)
- **Reason:** **Definition of midpoint**

Since \( X \) is the midpoint, by definition, it divides \( \overline{WY} \) into two equal segments \( WX \) and \( XY \). This is correct.

#### Step 3:
- **Statement:** \( WX \cong XZ \)
- **Reason:** **Definition of congruence**

This is incorrect. The correct reason for step 3 is **Given** because the problem explicitly states that \( WX \cong XZ \) as a given piece of information.

#### Step 4:
- **Statement:** \( WX = XZ \)
- **Reason:** **Definition of congruence**

This is correct. The definition of congruence allows you to state that if segments are congruent, then their lengths are equal.

#### Step 5:
- **Statement:** \( XY = XZ \)
- **Reason:** **Transitive property**

This is correct. The transitive property allows you to state that if \( WX = XY \) (from step 2) and \( WX = XZ \) (from step 4), then \( XY = XZ \).

#### Step 6:
- **Statement:** \( \overline{XY} \cong \overline{XZ} \)
- **Reason:** **Definition of congruence**

This is correct. Since their lengths are equal (from step 5), you can conclude that the segments are congruent by the definition of congruence.

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### Final Reasons List:
1. **Given**
2. **Definition of midpoint**
3. **Given** (This was incorrectly written as "Definition of congruence")
4. **Definition of congruence**
5. **Transitive property**
6. **Definition of congruence**

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Would you like more details on any step? Here are some questions for further understanding:

1. What is the difference between congruence and equality in geometry?
2. How does the transitive property work in geometric proofs?
3. Can a midpoint exist without creating congruent segments?
4. How do we use the definition of congruence in both directions?
5. Why is it important to write the correct reason for each statement?

**Tip:** Always remember to distinguish between "given" information and definitions or properties when writing reasons in geometric proofs.

Check my work and give me the answers for the reasons in this geometric proof where X is the midpoint of line segment WY, proving that XY ≅ XZ.

Review a step-by-step solution to a geometric proof demonstrating that if X is the midpoint of line segment WY, then XY is congruent to XZ. This proof covers key geometry concepts such as the definition of midpoint, transitive property, and the definition of congruence, suitable for students in Grades 8-10.

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