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:

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.