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Over Lesson 2–6 5-Minute Check 1 A.Distributive Property B.Addition Property C.Substitution Property D.Multiplication Property State the property that justifies the statement. 2(LM + NO) = 2LM + 2NO

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Over Lesson 2–6 5-Minute Check 2 A.Distributive Property B.Substitution Property C.Addition Property D.Transitive Property State the property that justifies the statement. If m R = m S, then m R + m T = m S + m T.

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Over Lesson 2–6 5-Minute Check 3 A.Multiplication Property B.Division Property C.Distributive Property D.Substitution Property State the property that justifies the statement. If 2PQ = OQ, then PQ =

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Over Lesson 2–6 5-Minute Check 4 A.Reflexive Property B.Symmetric Property C.Transitive Property D.Substitution Property State the property that justifies the statement. m Z = m Z

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Over Lesson 2–6 5-Minute Check 5 A.Reflexive Property B.Symmetric Property C.Substitution Property D.Transitive Property State the property that justifies the statement. If BC = CD and CD = EF, then BC = EF.

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Over Lesson 2–6 5-Minute Check 6 A.x = x B.If x = 3, then x + 4 = 7. C.If x = 3, then 3 = x. D.If x = 3 and x = y, then y = 3. Which statement shows an example of the Symmetric Property?

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Then/Now You wrote algebraic and two-column proofs. Write proofs involving segment addition. Write proofs involving segment congruence.

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Concept

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Example 1 Use the Segment Addition Postulate 2. 3. 4. StatementsReasons 1.

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Example 1 6. 7. Proof: StatementsReasons 5. Use the Segment Addition Postulate 8.

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Example 1 Prove the following. Given:AC = AB AB = BX CY = XD Prove:AY = BD

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Example 1 1. Given AC = AB, AB = BX 1. 2. Transitive Property AC = BX 2. 3. Given CY = XD 3. 4. Addition PropertyAC + CY = BX + XD4. AY = BD 6. Substitution6. Proof: StatementsReasons Which reason correctly completes the proof? 5. ________________ AC + CY = AY; BX + XD = BD 5. ?

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Example 1 A.Addition Property B.Substitution C.Definition of congruent segments D.Segment Addition Postulate

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Concept

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Over Lesson 2–6 Assignment: 148/ 1-10,23-36 160/ 1-13,18-20,24-43

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Lesson 2.5 Proving Statements about Segments VOCABULARY A true statement that follows as a result of other true statements is called a theorem. A two-column.

Lesson 2.5 Proving Statements about Segments VOCABULARY A true statement that follows as a result of other true statements is called a theorem. A two-column.

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