Geom 2point5
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The document discusses proving statements about congruent segments through two-column proofs and paragraph proofs. It states three properties of segment congruence: the reflexive, symmetric, and transitive properties. It provides an example proof and explains that a proof uses known statements and logical steps to prove the statement being shown. Students are directed to practice a proof using the transitive property on page 106 problem 19.
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Geom 2point5
- 1. 2.5 Proving Statements about Segments Objectives: - Justify statements about congruent segments - Write reasons for steps in a proof
- 2. Properties of Congruent Segments A true statement that follows as a result of other true statements is called a theorem . All theorems must be proved. You can prove a theorem using a two-column proof . A two-column proof has numbered statements and reasons that show the logical order of an argument.
- 3. Properties of Segment Congruence Reflexive Symmetric Transitive For any segment AB, AB ~= AB If AB ~= CD, then CD ~= AB If AB ~= CD, and CD ~= EF, then AB ~= EF
- 4. Look at p. 102 Example 1
- 5. Paragraph proofs Write out the same reasons as you would in a two-column proof, but in paragraph form. If you go on to college majoring in math, you will do more paragraph proofs than 2-column.
- 6. Using Congruence of Segments Look at p. 103 Start by stating what you know LK = 5 JK = 5 Last statement should be what you are proving Logical steps in between
- 7. Do p. 106 #19 Why? Transitive Property of Segment Congruence