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Bellringer

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Algebraic Proof Chapter 2-6

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**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.

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Algebraic Properties

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**Example Solve 3(x – 2) = 42 Algebraic Steps Properties**

3(x – 2) = Given 3x – 6 = Distributive Property 3x – = Addition Property 3x = Substitution Property 3x/3 = 48/ Division Property X = Substitution Property

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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

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**Example If 3(x – 2) = 3, then x = 3 Statements Reasons**

3(x – 2) = Given 3x – 6 = Distributive property 3x – = Addition property 3x = Substitution property 3x/3 = 9/ Division Property X = Substitution property

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Geometry proof

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**Example Given: m 2 = 60 1 is congruent to 2 Prove m 1 = 60**

Statement Reasons m 2 = Given M 2 = m Definition of congruence 60 = m Substitution M 1 = Symmetric Property

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