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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
2-4 Reasoning in Algebra

Objectives:

  • Use basic properties of algebra in reasoning
  • Define congruence
  • State the properties of congruence
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