Algebra Class 6: Algebraic Proofs

Study Notes

Algebraic Proof

Composed of a series of algebraic properties used to demonstrate the validity of statements.

Addition Property of Equality

Establishes that adding the same value to both sides of an equation maintains equality: if a = b, then a + c = b + c.

Subtraction Property of Equality

States that subtracting the same value from both sides of an equation preserves equality: if a = b, then a - c = b - c.

Multiplication Property of Equality

Indicates that multiplying both sides of an equation by the same non-zero value keeps equality intact: if a = b, then a × c = b × c.

Division Property of Equality

Asserts that dividing both sides of an equation by the same non-zero value maintains equality: if a = b and c ≠ 0, then a ÷ c = b ÷ c.

Reflexive Property of Equality

Confirms that any quantity is equal to itself: a = a.

Symmetric Property of Equality

Demonstrates that if one quantity equals another, the reverse is also true: if a = b, then b = a.

Transitive Property of Equality

Describes the relationship among three quantities: if a = b and b = c, then it follows that a = c.

Substitution Property of Equality

Allows for the replacement of one quantity with another in expressions or equations when they are known to be equal: if a = b, a can be substituted for b.

Distributive Property

Facilitates the distribution of multiplication over addition: a(b + c) = ab + ac.

Two-Column / Formal Proof

A structured form of proof that organizes statements and reasons into two distinct columns for clarity.

Description

This quiz focuses on various algebraic proofs and their properties. It covers key concepts such as the Addition, Subtraction, Multiplication, and Division Properties of Equality. Test your knowledge on these fundamental algebraic principles.