The document discusses various properties from algebra that students should learn, including: - The properties of equality like addition, subtraction, multiplication, and division properties - The reflexive, symmetric, and transitive properties - The distributive property - Properties of congruence It instructs students to write down these properties so they can be discussed and used in class the next day.

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2-2 Properties from Algebra
Please write down the properties
on these slides so that we may
discuss them and use them
tomorrow.

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Properties to Know
• When in the “number world” we can use the
real number properties from Algebra.
• The Properties of Equality that we will use
most often are:

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• Addition Property If a = b and c = d, then
a + c = b + d.
• Subtraction Property If a = b and c = d, then
a c = b d.
• Multiplication Property If a = b, then ca = cb.
• Division Property If a = b and c 0, then
• Substitution Property If a = b, then either a or b
may be substituted for the
other in any equation (or
inequality).
Properties from Algebra
.
a b
c c

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More Properties of Algebra
• Reflexive Property a = a
• Symmetric Property If a = b, then b = a.
• Transitive Property If a = b and b = c, then
a = c.

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The Distributive Property
For the real number system:
• a(b + c) = ab + ac
• (a + b)c = ac + bc
Solve 3x = 6 – ½x and justify each step.

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Properties of Congruence

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Take Note:
• There is NO Substitution Property of
Congruence!
• To use the Substitution Property, you
MUST be in the “number world.”