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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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Algebraic Proofs. 1. Transitive property of equality 2. Symmetric property of equality 3. Reflexive property of equality 4. Substitution 5. Addition property.

Algebraic Proofs. 1. Transitive property of equality 2. Symmetric property of equality 3. Reflexive property of equality 4. Substitution 5. Addition property.

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