Chapter 2.5 Notes: Reason Using Properties from Algebra

Goal: You will use algebraic properties in logical arguments.

• Algebraic Properties of Equality:• Addition Property:

x – 5 = 9

• Subtraction Property:x + 9 = -21

• Multiplication Property:2

83x

• Division Property:9x = -72

• Substitution Property:y = 3x – 5 when x = -2

• Distributive Property:-3(x – 5)

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.

• 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 _______________

7m m A

m A m B

• Transitive Property of EqualityIf a = b and ____ = c, then ___________If AB = CD and ____ = EF, then AB = ________If and ____ = , then ________. m A m B m C

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.

m EBA m DBC

• 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:

6 7m m 7 6m m

m W m W