1 2.5:Reason Using Properties from Algebra Goal:Use algebraic properties in logical arguments.

2 Algebraic Properties of Equality Let a, b, and c be real numbers.

3 Example 1:Write reasons for each step

4

5 Distributive Property a ( b + c ) = a aa ab + ac, where a, b, and c are real numbers.

6 Example 2:Use the Distributive Property

7 Checkpoint

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9 Example 3:Use properties in the real world Speed:A motorist travels 5 miles per hour slower than the speed limit s for 3.5 hours. The distance traveled d can be determined by the formula d = 3.5( s – 5). Solve for s.

10 Example 3:Use properties in the real world

11 Reflexive Property of Equality

12 Symmetric Property of Equality

13 Transitive Property of Equality

14 Example 4:Use properties of equality

15 Example 4:Use properties of equality

16 Checkpoint

17 Checkpoint:Name the property of equality

18 Checkpoint:Name the property of equality

19 Checkpoint:Name the property of equality