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2.4 Reasoning with Properties from Algebra

2.4 Reasoning with Properties from Algebra. Use properties of Algebra. Properties of Algebra. Addition Property If a = b, then a + c = b + c If x – 4 = 20, then x – 4 + 4 = 20 + 4. Properties of Algebra. Multiplication Property If a = b, then a * c = b * c where c ≠ 0

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2.4 Reasoning with Properties from Algebra

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  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 Property x = 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 – 18 Given

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

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

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

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

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

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

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

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

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

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

  17. Since this is Geometry, we will show Geometry facts with Algebra Given A B C D ; AC = BD Verify that AB = CD AC = BD Given

  18. Since this is Geometry, we will show Geometry facts with Algebra Given A B C D ; AC = BD Verify that AB = CD AC = BD Given AC = AB + BC

  19. Since this is Geometry, we will show Geometry facts with Algebra Given A B C D ; AC = BD Verify that AB = CD AC = BD Given AC = AB + BC Segment Addition

  20. Since this is Geometry, we will show Geometry facts with Algebra Given A B C D ; AC = BD Verify that AB = CD AC = BD Given AC = AB + BC Segment Addition BD = BC + CD Segment Addition

  21. Since this is Geometry, we will show Geometry facts with Algebra Given A B C D ; AC = BD Verify that AB = CD AC = BD Given AC = AB + BC Segment Addition BD = BC + CD Segment Addition AB + BC = BC + CD

  22. Since this is Geometry, we will show Geometry facts with Algebra Given A B C D ; AC = BD Verify that AB = CD AC = BD Given AC = AB + BC Segment Addition BD = BC + CD Segment Addition AB + BC = BC + CD Substitution Prop.

  23. Since this is Geometry, we will show Geometry facts with Algebra Given A B C D ; AC = BD Verify that AB = CD AC = BD Given AC = AB + BC Segment Addition BD = BC + CD Segment Addition AB + BC = BC + CD Substitution Prop. BC = BC Reflexive Prop.

  24. Since this is Geometry, we will show Geometry facts with Algebra Given A B C D ; AC = BD Verify that AB = CD AC = BD Given AC = AB + BC Segment Addition BD = BC + CD Segment Addition AB + BC = BC + CD Substitution Prop. BC = BC Reflexive Prop. AB = CD Addition/ Subtraction Prop.

  25. Given Find #1. #1. Given

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

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

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

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

  30. Given Find #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

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