1. Chapter 2.5 Notes: Reason Using Properties from Algebra Goal: You will use algebraic properties in logical arguments.

2. Algebraic Properties of Equality: Addition Property: x – 5 = 9 Subtraction Property: x + 9 = -21 Multiplication Property:

3. Division Property: 9x = -72 Substitution Property: y = 3x – 5 when x = -2 Distributive Property: -3(x – 5)

4. Ex.1: Solve 2x + 5 = 20 – 3x. Write a reason for each step. Ex.2: Solve -4(11x + 2) = 80. Write a reason for each step. Ex.3: Solve 14x + 3(7 – x) = -1. Write a reason for each step.

5. Properties: Reflexive Property of Equality: a = ____ i.e. 3 = ____ AB = ____ i.e. GH = ____ _____ i.e. ____ Symmetric Property of Equality: If a = b, then _____________ If AB = CD, then ________________ If, then _______________

6. Transitive Property of Equality If a = b and ____ = c, then ___________ If AB = CD and ____ = EF, then AB = ________ If and ____ =, then ________.

7. Ex.4: You are designing a logo to sell daffodils. Use the information given. Determine whether. Ex.5: In the diagram, AB = CD. Show that AC = BD.

8. Name the property of equality the statement illustrates. Ex.6: If, then. Ex.7: If JK = KL, and KL = 12, then JK = 12. Ex.8: