# 2-4 Reasoning in Algebra - PowerPoint PPT Presentation

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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

Objectives:

• Use basic properties of algebra in reasoning

• Define congruence

• State the properties of congruence

### 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

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

• 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