Key Concepts: Algebraic Proof

Properties of Equality

These algebraic properties are used to justify steps in proofs:

• Reflexive Property: a = a
• Symmetric Property: If a = b, then b = a
• Transitive Property: If a = b and b = c, then a = c
• Addition Property: If a = b, then a + c = b + c
• Subtraction Property: If a = b, then a − c = b − c
• Multiplication Property: If a = b, then ac = bc
• Division Property: If a = b and c ≠ 0, then a/c = b/c
• Substitution Property: If a = b, then a may replace b in any expression
• Distributive Property: a(b + c) = ab + ac