Algebraic Proofs

What is the Division Property of Equality?

• If a = b and c ≠ 0, then a / c = b / c.

• If a + b = c, then a = c - b.

• If a = b, then a + c = b + c.

• If a * b = c, then a = c / b.

Identify the property used here: 5x = 5x

• Reflexive Property of Equality

• Transitive Property of Equality

• Symmetric Property of Equality

• Substitution Property of Equality

What is the Symmetric Property of Equality?

• If a = b, then b = a.

• If a = b, then a + c = b + c.

• If a = b, then a - c = b - c.

• If a = b, then a * c = b * c.

What is reason 3 in a proof?

• Addition Property of Equality

• Subtraction Property of Inequality

• Multiplication Property of Zero

• Division Property of Equality

What is the Addition Property of Equality?

• If a = b, then a + c = b + c.

• If a + b = c, then a = c - b.

• If a = b, then a - c = b - c.

• If a + c = b, then a = b - c.

Identify the property used here: 39=39

• Reflexive

• Symmetric

• Transitive

• Associative

What is a postulate?

• A statement accepted without proof as a basis for reasoning.

• A theory that has been proven through experimentation.

• A hypothesis that requires further testing.

• A conclusion drawn from empirical evidence.

What is the purpose of a proof?

• To demonstrate the validity of a mathematical statement or theorem.

• To provide a visual representation of a concept.

• To summarize the findings of a research study.

• To entertain the audience with mathematical puzzles.

What is a theorem?

• A statement that has been proven based on previously established statements.

• A hypothesis that has not yet been tested.

• An opinion that is widely accepted as true.

• A mathematical expression that represents a relationship.

What is the Multiplication Property of Equality?

• If a = b, then a * c = b * c.

• If a + b = c, then a = c - b.

• If a = b, then a / c = b / c.

• If a * b = c, then a + b = c.