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

2. 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 _______________

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

4. 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:

5. 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

6. 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

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

8. 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

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

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