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### Proofs in Algebra: Properties of Equality

• Additional Property of Equality: For all numbers a, b, and c, if a = b, then a + c = b + c
• Subtraction Property of Equality: For all numbers a, b, and c, if a = b, then a – c = b – c
• Multiplication Property of Equality: For all numbers a, b, and c, if a = b, then a × c = b × c
• Division Property of Equality: For all numbers a, b, and c, if a = b, then a/c = b/c
• Reflexive Property of Equality: For every number a, a = a
• Symmetric Property of Equality: For all numbers a and b, if a = b, then b = a
• Transitive Property of Equality: For all numbers a, b, and c, if a = b and b = c, then a = c
• Substitution Property of Equality: For all numbers a and b, if a = b, then a may be replaced by b in any equation or expression
• Distribute Property of Equality: For all numbers a, b, and c, a(b + c) = ab + ac
• One way to organize deductive reasoning is by using a two-column proof

## Proofs in Algebra: Properties of Equality

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