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**2-5 Reasoning in Algebra and Geometry**

Objective: To connect reasoning in algebra and geometry Essential Understanding: Algebraic properties of equality are used in geometry. They will help you solve problems and justify each step you take.

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**Key Concept Properties of Equality**

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…another Key Concept

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**Example: Solve for x. Give reason for each step.**

You use deductive reasoning when you solve an equation. You can justify each step with a postulate, a property, or a definition. Example: Solve for x. Give reason for each step. 3(2x + 1) + 2(2x +1) + 7 = 42 – 5x Given 6x x = 42 – 5x Distributive Property 10x + 12 = 42 – 5x Combine Like terms 15x + 12 = 42 Addition Property of Equality 15x = 30 Subtraction Property of Equality x = 2 Division Property of Equality

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**What is the value of x? Justify each step.**

x = 2x - 75 Definition of an angle bisector. x + 75 = 2x Addition Property of Equality. 75 = 2x - x Subtraction Property of Equality. x = 75 Distributive Property

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**Properties of Congruence:**

Reflexive Property Symmetric Property Transitive Property

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**p. 117: 5-11 odd [write both columns in each problem]**

Page 115 a. Symmetric Property b. Distributive Property c. Multiplication Property d. Reflexive Property p. 117: 5-11 odd [write both columns in each problem]

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