Chapter 2 Review Proofs in Algebra. Vocabulary Addition and Subtraction Properties Multiplication and Division Properties Substitution Property Commutative.

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Presentation transcript:

Chapter 2 Review Proofs in Algebra

Vocabulary Addition and Subtraction Properties Multiplication and Division Properties Substitution Property Commutative Properties Associative Properties Distributive Property Reflexive Property Symmetric Property Transitive Property

Vocabulary Segment Addition Postulate Overlapping segments Overlapping Segments Theorem Segment bisector Midpoint Perpendicular bisector

Name the property of equality that justifies each statement. a. If x = 4, then x ● 2 = 4 ● 2. b. If 5b = 10, then b = 2. c. d. If x – y = 2, then x = y + 2 e. If AB = 3y and AB = CD, then 3y = CD. f. If a = b, then b = a. g. 2 = 2

Name the property of equality that justifies each statement. a. (3 + 2) + 5 = 3 + (2 + 5) b. If AC = XY and BD = UV, then AC + BD = XY + UV c. 2r + 3r = 5r d. S + (t + u) = (t + u) + s e. If 3x = 9 and x = 3, then 3(3) = 9 f. If 3x + 2 = 17, then 3x = 15. g. If AC + BC = BC + DE, then AC = DE.

Identify the errors in the following proof: If 2x + 4 = 12, then x = 4. StatementsReasons a. 2x + 4 = 12a.Given b. 4 = 4b. Substitution property c. 2x = 8c. Addition Property of Equality d. 2=2 d. Reflexive Property e. x = 16e. Division property

Complete a proof for the following: If 5x = 9+2x, then x = 3. StatementsReasons

Complete a proof for the following: Given: AP = BP; PC = PD Prove: AC = BD StatementsReasons

Complete a proof for the following: Given: M bisects ; MB = BC Prove: AB = MC StatementsReasons a. M bisectsa. Given b. M is the midpoint ofb. c.c. Definition of midpoint d. AM = MBd. e. MB = BCe. f.f. Transitive Property of Equality g. AB = MCg.