1. 2-5 Algebraic proofs

2. SAT Problem of the day The volume and surface area of a cube are equal. What is the length of an edge of this cube? A) 1 B) 2 C)4 D)6 E)9

3. SAT problem of the day Answer :D

4. Objectives * Review properties of equality and use them to write algebraic proofs. *Identify properties of equality and congruence.

5. What are Proofs? A proof is an argument that uses logic, definitions, properties, and previously proven statements to show that a conclusion is true. An important part of writing a proof is giving justifications to show that every step is valid.

6. Properties

7. The Distributive Property states that: a(b + c) = ab + ac.

8. Example#1 Solve the equation 4m – 8 = –12. Write a justification for each step. 4m – 8 = –12 Given equation +8 +8 Addition Property of Equality 4m = –4 Simplify. m =–1 Simplify. Division Property of Equality

9. Example#2 Solve the equation. Write a justification for each step. Given equationMultiplication Property of Equality. t = –14Simplify.

10. Example#3

11. Example#4

12. Student Guided Practice Do problems 2-7 on your book page 107

13. Applications

14. What is the temperature in degrees Celsius C when it is 86°F? Solve the equation C = 5/9(F – 32) for C and justify each step.

15. Algebraic proofs in geometry Like algebra, geometry also uses numbers, variables, and operations. For example, segment lengths and angle measures are numbers. So you can use these same properties of equality to write algebraic proofs in geometry.

16. Properties A ____________ B AB represents the length AB, so you can think of AB as a variable representing a number.

17. Geometric properties You learned in Chapter 1 that segments with equal lengths are congruent and that angles with equal measures are congruent. So the Reflexive, Symmetric, and Transitive Properties of Equality have corresponding properties of congruence.

19. Example#5 Write a justification for each step. NO = NM + MO

20. Example#6 Write a justification for each step. mABC = mABD + mDBC

21. Student Guided Practice Do Problems 10 and 11 from page 107 on your book

22. Homework!! Do problems 16-23 from page 108

23. Closure Today we learned about algebraic proofs and how to justify each step. Next class we are going to learned about geometric proofs