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The question asks to convert the given paragraph proof into a two-column proof format. Let's break it down step-by-step and present it in a two-column format.

### Given:
- \( AB = CD \)
- \( BC = DE \)

### To Prove:
- \( AC = CE \)

### Paragraph Proof Explanation:
- By the addition property of equality, adding \( BC \) to both sides of \( AB = CD \) gives \( AB + BC = CD + BC \).
- Given \( BC = DE \), we can substitute \( DE \) for \( BC \) in the equation, resulting in \( AB + DE = CD + DE \).
- Using segment addition, we observe that \( AB + BC = AC \) and \( CD + DE = CE \).
- Finally, substituting these values, we get \( AC = CE \).

### Two-Column Proof:

| **Statements**                        | **Reasons**                          |
|---------------------------------------|--------------------------------------|
| 1. \( AB = CD \)                      | 1. Given                             |
| 2. \( BC = DE \)                      | 2. Given                             |
| 3. \( AB + BC = CD + BC \)            | 3. Addition Property of Equality     |
| 4. \( AB + DE = CD + DE \)            | 4. Substitution Property of Equality |
| 5. \( AB + BC = AC \)                 | 5. Segment Addition Postulate        |
| 6. \( CD + DE = CE \)                 | 6. Segment Addition Postulate        |
| 7. \( AC = CE \)                      | 7. Substitution Property of Equality |

This proof structure is more formal and clear, adhering to the standard two-column proof method.

Would you like more details on the steps, or do you have any questions?

Here are 5 related questions:
1. Can you explain the Addition Property of Equality?
2. What is the Segment Addition Postulate?
3. How does the Substitution Property of Equality work in proofs?
4. Why is it important to have clear reasoning in a two-column proof?
5. How can this proof be applied to other geometric problems?

**Tip**: In geometry, always make sure to clearly state all given information and identify what needs to be proven before starting your proof.

Given: AB = CD and BC = DE. Prove: AC = CE

Learn how to solve a geometric proof problem where you are given AB = CD and BC = DE, and need to prove AC = CE. This step-by-step two-column proof covers important geometry concepts like the Addition Property of Equality, the Substitution Property of Equality, and the Segment Addition Postulate. Suitable for students in Grades 9-10.

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