Chapter 2.5-2.6 Notes: Properties and Algebraic Proofs Goal: You will use algebraic properties in logical arguments.

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 _______________

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

Name the property of equality the statement illustrates. Ex.1: If , then . Ex.2: If JK = KL, and KL = 12, then JK = 12. Ex.3:

Theorem 2.1 Congruence of Segments: Segment congruence is reflexive, symmetric, and transitive. Reflexive Property: For any segment AB, . Symmetric Property: If , then . Transitive Property: If and , then .

Theorem 2.2 Congruence of Angles: Angle congruence is reflexive, symmetric, and transitive. Reflexive Property: For any angle A, . Symmetric Property: If , then . Transitive Property: If and then .

Ex.4: Name the property illustrated by the statement. a. If and , then . b. If , then . c. d. If and , then .

Solve each equation. Show all your steps and write a reason for each step. Ex.5: 5(x + 3) = -4 Ex.6: ½ x – 5 = -10

Solve for the variable. Show all your steps and write a reason for each step. Ex.7: Given: Ex.8: Given: bisects

Ex.9: Given: AC = 21 Ex.10: Given: M is the midpoint of VW.