Bellringer.

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Presentation transcript:

Bellringer

Algebraic Proof Chapter 2-6

Algebraic Proof Algebraic proofs use properties to prove relationships Reflexive, Symmetric, Transitive, Addition and Subtraction, Multiplication and Division, Substitution, and Distributive Property A group of algebraic steps used to solve problems form a deductive argument.

Algebraic Properties

Example Solve 3(x – 2) = 42 Algebraic Steps Properties 3(x – 2) = 42 Given 3x – 6 = 42 Distributive Property 3x – 6 + 6 = 42 + 6 Addition Property 3x = 48 Substitution Property 3x/3 = 48/3 Division Property X = 16 Substitution Property

Two column proof A two-column proof, or formal proof contains statements and reasons organized in two columns. In a two column proof each step is called a statement and the properties that justify each step are called reasons

Example If 3(x – 2) = 3, then x = 3 Statements Reasons 3(x – 2) = 3 Given 3x – 6 = 3 Distributive property 3x – 6 + 6 = 3 + 6 Addition property 3x = 9 Substitution property 3x/3 = 9/3 Division Property X = 3 Substitution property

Geometry proof

Example Given: m 2 = 60 1 is congruent to 2 Prove m 1 = 60 Statement Reasons m 2 = 60 Given M 2 = m 1 Definition of congruence 60 = m 1 Substitution M 1 = 60 Symmetric Property

You Do