https://file.aiquickdraw.com/mathbot/file/1727788252458j213swhx.jpg

Let's review the two-column proof from the image and verify its correctness.

### Given:
- \( AB \cong CD \)
- \( CE \cong AE \)

### To Prove:
- \( ED \cong EB \)

### Proof:

| Statements                        | Reasons                              |
|------------------------------------|--------------------------------------|
| 1. \( AB \cong CD \)               | 1. Given                             |
| 2. \( AB \cong CE \cong AE \)      | 2. Definition of congruence          |
| 3. \( AE + EB = AB; CE + ED = CD \) | 3. Segment addition postulate        |
| 4. \( CE + ED = CE + EB \)         | 4. Substitution                      |
| 5. \( CE + ED = CD \)              | 5. Transitive                        |
| 6. \( ED = EB \)                   | 6. Subtraction                       |
| 7. \( ED \cong EB \)               | 7. Definition of congruence          |

### Verification:

- **Step 1**: Correct, as it simply states the given information.
- **Step 2**: This is valid; congruent segments maintain their equality, and the reason refers to the definition of congruence.
- **Step 3**: This is the application of the **Segment Addition Postulate**, which states that if point E is between A and B, then \( AE + EB = AB \), and similarly for the other segment.
- **Step 4**: Substitution is properly used here to replace congruent segments.
- **Step 5**: Transitive property is correctly applied.
- **Step 6**: The subtraction of the same length on both sides is valid here.
- **Step 7**: The final step, stating that \( ED \cong EB \), follows from the definition of congruence, which completes the proof.

### Conclusion:
The proof looks **correct**. Each step logically follows from the previous one, and the reasons provided are appropriately aligned with the statements.

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Would you like more details on any particular step? Here are 5 follow-up questions:

1. Can you explain more about the Segment Addition Postulate used in Step 3?
2. How is the transitive property applied in geometry proofs?
3. Could you break down the substitution process in Step 4?
4. What is the significance of the subtraction step in Step 6?
5. How does the final step use the definition of congruence to conclude the proof?

**Tip**: In geometry, clearly understanding each theorem and postulate will help you solve proofs more easily.

Review a geometry proof that uses the Segment Addition Postulate and the Transitive Property to prove ED ≅ EB, based on given congruent segments AB ≅ CD and CE ≅ AE. Suitable for high school geometry students, Grades 9-11.

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