1. Lesson 2-6 Algebraic Proofs

2. Ohio Content Standards:

3. Establish the validity of conjectures about geometric objects, their properties and relationships by counter-example, inductive and deductive reasoning, and critiquing arguments made by others.

4. Ohio Content Standards: Make and test conjectures about characteristics and properties (e.g., sides, angles, symmetry) of two-dimensional figures and three- dimensional objects.

5. Ohio Content Standards: Make, test and establish the validity of conjectures about geometric properties and relationships using counterexample, inductive and deductive reasoning, and paragraph or two-column proof.

6. Reflexive Property

7. For every number a = a.

8. Symmetric Property

9. For all numbers a and b, if a = b, then b = a.

10. Transitive Property

11. For all numbers a, b, and c, if a = b and b = c, then a = c.

12. Addition and Subtraction Properties

13. For all numbers a, b, and c, if a = b, then a + c = b + c and a – c = b – c.

14. Multiplication and Division Properties

15. For all numbers a, b, and c, if a = b, then a ∙ c = b ∙ c and if c = 0,

16. Substitution Property

17. For all numbers a and b, if a = b, then a may be replaced by b in any equation or expression.

18. Distributive Property

19. For all numbers a, b, and c, a(b + c) = ab + ac.

20. Deductive Argument

21. A group of algebraic steps used to solve problems.

22. Solve. 2(5 – 3a) – 4(a + 7) = 92

23. Two-Column Proof (Formal Proof)

24. Contains statements and reasons organized in two columns.

25. Write a two-column proof.

27. Assignment: Pgs. 97 - 100 14-23 all, 24-30 evens 40-46 evens