2.4 reasoning with properties from algebra
DESCRIPTION
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 - PowerPoint PPT PresentationTRANSCRIPT
2.4 Reasoning with 2.4 Reasoning with Properties from Properties from
AlgebraAlgebraUse properties of AlgebraUse 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
If ⅛ x = 4, then 8 * ⅛ x = 4 * 8
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
More properties in Algebra
Substitution Property
If x = 4, then 3x + 2 = 3(4) + 2
Distributive Property
2(x + 4) = 2x + 2(4)
Using the property of Algebra to solve an equation
3x + 12 = 8x – 18 Given
Using the property of Algebra to solve an equation
3x + 12 = 8x – 18 Given
- 3x = - 3x Reflexive Property
Using the property of Algebra to solve an equation
3x + 12 = 8x – 18 Given
- 3x = - 3x Reflexive Property
3x – 3x + 12 = 8x – 3x – 18Add. Property
Using the property of Algebra to solve an equation
3x + 12 = 8x – 18 Given
- 3x = - 3x Reflexive Property
3x – 3x + 12 = 8x – 3x – 18Add. Property
12 = 5x -18 Simplified
Using the property of Algebra to solve an equation
3x + 12 = 8x – 18 Given
- 3x = - 3x Reflexive Property
3x – 3x + 12 = 8x – 3x – 18Add. Property
12 = 5x -18 Simplified
18 = 18 Reflexive Property
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
Using the property of Algebra to solve an equation
3x + 12 = 8x – 18 Given - 3x = - 3x Reflexive Property
3x – 3x + 12 = 8x – 3x – 18Add. Property12 = 5x -18 Simplified18 = 18 Reflexive Property
12 + 18 = 5x – 18 + 18 Add. Property30 = 5x Simplified
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. Property12 = 5x -18 Simplified18 = 18 Reflexive Property
12 + 18 = 5x – 18 + 18 Add. Property30 = 5x Simplified
1/5 = 1/5 Reflexive Property
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. Property12 = 5x -18 Simplified18 = 18 Reflexive Property
12 + 18 = 5x – 18 + 18 Add. Property30 = 5x Simplified
1/5 = 1/5 Reflexive Property30 * 1/5 = 5x * 1/5 Mult. Property
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. Property12 = 5x -18 Simplified18 = 18 Reflexive Property
12 + 18 = 5x – 18 + 18 Add. Property30 = 5x Simplified
1/5 = 1/5 Reflexive Property30 * 1/5 = 5x * 1/5 Mult. Property
6 = x Simplified
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. Property12 = 5x -18 Simplified18 = 18 Reflexive Property
12 + 18 = 5x – 18 + 18 Add. Property30 = 5x Simplified
1/5 = 1/5 Reflexive Property30 * 1/5 = 5x * 1/5 Mult. Property
6 = x Simplifiedx = 6 Symmetric Property
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
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
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
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
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
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.
Since this is Geometry, we will show Geometry facts with Algebra
Given A B C D ; AC = BD Verify that AB = CD
AC = BD GivenAC = AB + BC Segment AdditionBD = BC + CD Segment AdditionAB + BC = BC + CD Substitution Prop.BC = BC Reflexive Prop.
Since this is Geometry, we will show Geometry facts with Algebra
Given A B C D ; AC = BD Verify that AB = CD
AC = BD GivenAC = AB + BC Segment AdditionBD = BC + CD Segment AdditionAB + BC = BC + CD Substitution Prop.BC = BC Reflexive Prop.AB = CD Addition/ Subtraction
Prop.
Given Find
#1. #1. Given
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180321
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Given Find
#1. #1. Given
#2. #2. Subst. Prop
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4m
18043
180321
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mmm
43321 mmmmm
Given Find
#1. #1. Given
#2. #2. Subst. Prop
#3. #3. Reflex Prop.
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180321
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4m
18043
180321
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mmm
43321 mmmmm
33 mm
Given Find
#1. #1. Given
#2. #2. Subst. Prop
#3. #3. Reflex Prop.
#4. #4. Add./Subt Prop.
18043
9321
180321
mm
mm
mmm
4m
18043
180321
mm
mmm
43321 mmmmm
33 mm
421 mmm
Given Find
#1. #1. Given
#2. #2. Subst. Prop
#3. #3. Reflex Prop.
#4. #4. Add./Subt. Prop.
#5. #5. Given
18043
9321
180321
mm
mm
mmm
4m
18043
180321
mm
mmm
43321 mmmmm
33 mm
421 mmm
9321 mm
Given Find
#1. #1. Given
#2. #2. Subst. Prop
#3. #3. Reflex Prop.
#4. #4. Add./Subt. Prop.
#5. #5. Given
#6. #6. Substitution
18043
9321
180321
mm
mm
mmm
4m
18043
180321
mm
mmm
43321 mmmmm
33 mm
421 mmm
9321 mm
493 m
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