2-6 Algebraic Proof Ms. Andrejko.

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Presentation transcript:

2-6 Algebraic Proof Ms. Andrejko

Real World Mythbusters

Vocabulary Algebraic Proof- uses a group of algebraic steps to solve problems and justify each step. Two-column proof/formal proof- contains statements and reasons organized into 2 columns

Properties (see handout) Addition property of equality Subtraction property of equality Multiplication property of equality Division property of equality Reflexive property of equality Symmetric property of equality Transitive property of equality Substitution property of equality Distributive property

Examples – Find property State the property that justifies each statement: If 80 = m∠A, then m∠A = 80. If RS = TU and TU = YP, then RS = YP Reflexive Property of Equality Transitive Property of Equality

Practice – Find property State the property that justifies each statement: If 7x = 28, then x = 4. If VR + TY = EN + TY, then VR = EN. If m∠1 = 30 and m∠1 = m∠2, then m∠2 = 30. Division Property of Equality Subtraction Property of Equality Transitive Property of Equality

Example – Fill in proof Given Subtraction Prop. 6x -5 = 1 Substitution Prop. Division Prop. X=1 Substitution Prop.

Practice – Fill in the Proof STATEMENTS REASONS a. DF ≅ EG a. b. b. Definition of Congruence c. 11 = 2x-9 c. d. d. Addition prop. e. 20 = 2x f. f. Division Prop. g. Given DF = EG Substitution Prop. Given: DF ≅ EG Prove: x=10 11+9 = 2x-9+9 Substitution Prop. (20/2) = (2x/2) 10 = x Substitution Prop.

Practice – Fill in proof Given: Prove: x = - 40 Proof: STATEMENTS REASONS a. a. Given b. c. 8-3x = 128 c. d. d. Subtraction property e. -3x = 120 e. f. X = - 40 f. Multiplication Prop. Substitution Prop. 8-3x-8 = 128-8 Substitution Prop. Division Prop.