1. 2.4 Reasoning with Properties from Algebra Use properties of Algebra

2. Properties of Algebra Addition Property If a = b, then a + c = b + c If x – 4 = 20, then x – 4 + 4 = 20 + 4

3. Properties of Algebra Multiplication Property If a = b, then a * c = b * c where c ≠ 0 If ⅛ x = 4, then 8 * ⅛ x = 4 * 8

4. Other properties in Algebra Reflexive Propertyx = x Symmetric Property If a = b, then b = a Transitive Property If a = b and b = c, then a = c

5. More properties in Algebra Substitution Property If x = 4, then 3x + 2 = 3(4) + 2 Distributive Property 2(x + 4) = 2x + 2(4)

6. Using the property of Algebra to solve an equation 3x + 12 = 8x – 18Given

7. Using the property of Algebra to solve an equation 3x + 12 = 8x – 18Given - 3x = - 3xReflexive Property

8. Using the property of Algebra to solve an equation 3x + 12 = 8x – 18Given - 3x = - 3xReflexive Property 3x – 3x + 12 = 8x – 3x – 18Add. Property

9. Using the property of Algebra to solve an equation 3x + 12 = 8x – 18Given - 3x = - 3xReflexive Property 3x – 3x + 12 = 8x – 3x – 18Add. Property 12 = 5x -18Simplified

10. Using the property of Algebra to solve an equation 3x + 12 = 8x – 18Given - 3x = - 3xReflexive Property 3x – 3x + 12 = 8x – 3x – 18Add. Property 12 = 5x -18Simplified 18 = 18Reflexive Property

11. Using the property of Algebra to solve an equation 3x + 12 = 8x – 18Given - 3x = - 3xReflexive Property 3x – 3x + 12 = 8x – 3x – 18Add. Property 12 = 5x -18Simplified 18 = 18Reflexive Property 12 + 18 = 5x – 18 + 18Add. Property

12. Using the property of Algebra to solve an equation 3x + 12 = 8x – 18Given - 3x = - 3xReflexive Property 3x – 3x + 12 = 8x – 3x – 18Add. Property 12 = 5x -18Simplified 18 = 18Reflexive Property 12 + 18 = 5x – 18 + 18Add. Property 30 = 5xSimplified

13. Using the property of Algebra to solve an equation 3x + 12 = 8x – 18Given - 3x = - 3xReflexive Property 3x – 3x + 12 = 8x – 3x – 18Add. Property 12 = 5x -18Simplified 18 = 18Reflexive Property 12 + 18 = 5x – 18 + 18Add. Property 30 = 5xSimplified 1/5 = 1/5Reflexive Property

14. Using the property of Algebra to solve an equation 3x + 12 = 8x – 18Given - 3x = - 3xReflexive Property 3x – 3x + 12 = 8x – 3x – 18Add. Property 12 = 5x -18Simplified 18 = 18Reflexive Property 12 + 18 = 5x – 18 + 18Add. Property 30 = 5xSimplified 1/5 = 1/5Reflexive Property 30 * 1/5 = 5x * 1/5Mult. Property

15. Using the property of Algebra to solve an equation 3x + 12 = 8x – 18Given - 3x = - 3xReflexive Property 3x – 3x + 12 = 8x – 3x – 18Add. Property 12 = 5x -18Simplified 18 = 18Reflexive Property 12 + 18 = 5x – 18 + 18Add. Property 30 = 5xSimplified 1/5 = 1/5Reflexive Property 30 * 1/5 = 5x * 1/5Mult. Property 6 = xSimplified

16. Using the property of Algebra to solve an equation 3x + 12 = 8x – 18Given - 3x = - 3xReflexive Property 3x – 3x + 12 = 8x – 3x – 18Add. Property 12 = 5x -18Simplified 18 = 18Reflexive Property 12 + 18 = 5x – 18 + 18Add. Property 30 = 5xSimplified 1/5 = 1/5Reflexive Property 30 * 1/5 = 5x * 1/5Mult. Property 6 = xSimplified x = 6Symmetric Property

17. Since this is Geometry, we will show Geometry facts with Algebra GivenABCD ; AC = BDVerify that AB = CD AC = BDGiven

18. Since this is Geometry, we will show Geometry facts with Algebra GivenABCD ; AC = BDVerify that AB = CD AC = BDGiven AC = AB + BC

19. Since this is Geometry, we will show Geometry facts with Algebra GivenABCD ; AC = BDVerify that AB = CD AC = BDGiven AC = AB + BCSegment Addition

20. Since this is Geometry, we will show Geometry facts with Algebra GivenABCD ; AC = BDVerify that AB = CD AC = BDGiven AC = AB + BCSegment Addition BD = BC + CDSegment Addition

21. Since this is Geometry, we will show Geometry facts with Algebra GivenABCD ; AC = BDVerify that AB = CD AC = BDGiven AC = AB + BCSegment Addition BD = BC + CDSegment Addition AB + BC = BC + CD

22. Since this is Geometry, we will show Geometry facts with Algebra GivenABCD ; AC = BDVerify that AB = CD AC = BDGiven AC = AB + BCSegment Addition BD = BC + CDSegment Addition AB + BC = BC + CDSubstitution Prop.

23. Since this is Geometry, we will show Geometry facts with Algebra GivenABCD ; AC = BDVerify that AB = CD AC = BDGiven AC = AB + BCSegment Addition BD = BC + CDSegment Addition AB + BC = BC + CDSubstitution Prop. BC = BCReflexive Prop.

24. Since this is Geometry, we will show Geometry facts with Algebra GivenABCD ; AC = BDVerify that AB = CD AC = BDGiven AC = AB + BCSegment Addition BD = BC + CDSegment Addition AB + BC = BC + CDSubstitution Prop. BC = BCReflexive Prop. AB = CDAddition/ Subtraction Prop.

25. GivenFind #1.#1.Given

26. GivenFind #1.#1.Given #2.#2.Subst. Prop

27. GivenFind #1.#1.Given #2.#2.Subst. Prop #3.#3.Reflex Prop.

28. GivenFind #1.#1.Given #2.#2.Subst. Prop #3.#3.Reflex Prop. #4.#4. Add./Subt Prop.

29. GivenFind #1.#1.Given #2.#2.Subst. Prop #3.#3.Reflex Prop. #4.#4. Add./Subt. Prop. #5.#5.Given

30. GivenFind #1.#1.Given #2.#2.Subst. Prop #3.#3.Reflex Prop. #4.#4. Add./Subt. Prop. #5.#5.Given #6.#6.Substitution

31. Homework Page 99 – 101 # 10 - 25, 27, 32 # 10 - 25, 27, 32