2 6 Algebraic Proof Ms Andrejko Real World

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: 1. If 80 = m∠A, then m∠A = 80. Reflexive Property of Equality 2. If RS = TU and TU = YP, then RS = YP Transitive Property of Equality

Practice – Find property �State the property that justifies each statement: 1. If 7 x = 28, then x = 4. Division Property of Equality 2. If VR + TY = EN + TY, then VR = EN. Subtraction Property of Equality 3. If m∠ 1 = 30 and m∠ 1 = m∠ 2, then m∠ 2 = 30. Transitive Property of Equality

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

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

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