1. 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.

2. Key Concept Properties of Equality

3. …another Key Concept

4. 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

5. 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

6. Properties of Congruence:
Reflexive Property
Symmetric Property
Transitive Property

7. 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]