# Honors Geometry Companion Book, Volume 1

2.2.3 Flowchart and Paragraph Proofs (continued)

In this example, the conjecture, figure, and paragraph proof are given and then a two-column proof is written based on the paragraph proof. The order of the steps in the two-column proof does not have to exactly match the order of the corresponding sentences from the paragraph proof, but the order should be similar if not the same.

Example 3 Writing a Paragraph Proof The Common Segments Theorem states that given collinear points A , B , C , and D arranged on a segment such that A and D are the endpoints, B is between A and C , and C is between B and D . If AB ≅ CD , then AC ≅ BD . This theorem is proven in the example below.

In this example, the conjecture, figure, and two- column proof are given and then a paragraph proof is written based on the two-column proof. Each sentence in the paragraph proof is simply a combination of a statement and its corresponding reason from the two-column proof. The paragraph proof begins with the information given in the conjecture and ends with the conjecture’s conclusion.

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