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2-4 Reasoning in Algebra

2-4 Reasoning in Algebra. Objectives: Use basic properties of algebra in reasoning Define congruence State the properties of congruence. Properties of Equality. Solve and Write a Justification for Each Step. 2 (x + 1) = 8 Given 2x + 2 = 8 Distributive Property

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2-4 Reasoning in Algebra

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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

  2. Properties of Equality

  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 =

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

  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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