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1 2-4 Reasoning in Algebra Objectives: Use basic properties of algebra in reasoning Define congruence State the properties of congruence

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2 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 and c 0, then a/c = b/c 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 b can replace a in any expression Distributive Propertya(b + c) = ab + ac

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3 Solve and Write a Justification for Each Step 2 (x + 1) = 8 Given 2x + 2 = 8 Distributive Property 2x = 6 Subtraction Property of = x = 3 Division Property of =

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4 Congruence in Geometry Congruence – Having the same shape and size Symbol for congruence AB CD (Segment AB is congruent to segment CD.) ABCD A B (Angle A is congruent to angle B.) AB

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5 Properties of Congruence Reflexive Property AB AB A A Symmetric Property If AB CD, then CD AB If A B, then B A Transitive Property If AB CD and CD EF, then AB EF If A B and B C,then A C

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