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2-4 Reasoning in AlgebraPowerPoint Presentation

2-4 Reasoning in Algebra

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2-4 Reasoning in Algebra

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Objectives:

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

2 (x + 1) = 8 Given

2x + 2 = 8 Distributive Property

2x = 6 Subtraction Property of =

x = 3 Division Property of =

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.)

- 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