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September 8, 2011 "The way to be nothing is to do nothing." -- Nathaniel Howe Test prep, p. 18 #

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Reasoning in Algebra Properties of Equality

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1. Addition Property of Equality If a = b, then a + c = b + c Example: If x – 3 = -8, then x = -5

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2. Subtraction Property of Equality If a = b, the a – c = b – c Example: If 15 = a + 4, then 11 = a

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3. Multiplication Property of Equality If a = b, then a ( c ) = b ( c ) Example: If then r = 40

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4. Division Property of Equality If a = b, then Example: If 4c = -96, then c = -24

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5. Reflexive Property of Equality a = a Example: x + 3 = x + 3

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6. Symmetric Property: If a = b, then b = a Example: If 15 = 3t, then 3t = 15

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7. Transitive Property: If a = b and b = c, then a = c Example: If d = 3y and 3y = 6, then d = 6

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8. Substitution Property: If a = b, then b can replace a in any expression. Example: If x = 10, then x + y = 10 + y

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9. Distributive Property a(b + c) = ab + ac Example: 5(4 + 2) =

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Properties of Congruence

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1.Reflexive Property of Congruence

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2.Symmetric Property of Congruence If then

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3.Transitive Property of Congruence If and then

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Solve 5x – 12 = 32 + x for x 1. 5x-12 = 32 + x 5x = 44 + x 2.4x = x = 11 Given Addition Property of Equality Subtraction Property of Equality Division Property of Equality

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AB + BC = AC (4 + 2x) + (15 – x) = x = 21 X = 2 Segment Addition Postulate Substitution Property of Equality Simplify Subtraction Property of Equality If AC = 21, solve for x

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