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• 1 is congruent to 2• M 2 = m 1 Definition of

congruence• 60 = m 1 Substitution• M 1 = 60 Symmetric Property

You Do