2 4 reasoning in algebra
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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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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

Properties of Equality


Solve and write a justification for each step

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 =


Congruence in geometry

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.)


Properties of congruence

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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