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Chapter 2 Section 5

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Objective Students will make a connection between reasoning in Algebra and reasoning in Geometry.

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Properties of Equality Algebraic properties of equality are used in geometry to justify steps to solving problems.

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Properties of Equality 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 A · C = B · C Division Property If A = B then A ÷ C = B ÷ C (iff C ≠ 0)

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Properties of Equality Reflexive Property A = A Symmetric Property If A = B, then B = A Transitive Property If A = B and B = C, then A = C Substitution Property If A = B, then A can replace B in any expression.

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Distributive Property A ( B + C ) = AB + AC

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Page 114 Look at Problem 1

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Properties of Congruence Reflexive, Symmetric, and Transitive properties hold true for congruence the same as they do for equivalence. (See page 114 for examples of congruence properties).

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Proof A convincing argument that uses deductive reasoning It logically shows why a conjecture is true.

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Two-column Proof Lists each statement (or step) on the left and gives the justification on the right.

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Page 116 Look at Problem 3. Try the “Got It’ Problem 3.

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