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
![Page 1: 2.4 Reasoning with Properties from Algebra](https://reader033.vdocuments.net/reader033/viewer/2022061603/56813bf2550346895da5282b/html5/thumbnails/1.jpg)
2.4 Reasoning with 2.4 Reasoning with Properties from Properties from
AlgebraAlgebraUse properties of AlgebraUse properties of Algebra
![Page 2: 2.4 Reasoning with Properties from Algebra](https://reader033.vdocuments.net/reader033/viewer/2022061603/56813bf2550346895da5282b/html5/thumbnails/2.jpg)
Properties of Algebra
Addition Property
If a = b, then a + c = b + c
If x – 4 = 20, then x – 4 + 4 = 20 + 4
![Page 3: 2.4 Reasoning with Properties from Algebra](https://reader033.vdocuments.net/reader033/viewer/2022061603/56813bf2550346895da5282b/html5/thumbnails/3.jpg)
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
![Page 4: 2.4 Reasoning with Properties from Algebra](https://reader033.vdocuments.net/reader033/viewer/2022061603/56813bf2550346895da5282b/html5/thumbnails/4.jpg)
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
![Page 5: 2.4 Reasoning with Properties from Algebra](https://reader033.vdocuments.net/reader033/viewer/2022061603/56813bf2550346895da5282b/html5/thumbnails/5.jpg)
More properties in Algebra
Substitution Property
If x = 4, then 3x + 2 = 3(4) + 2
Distributive Property
2(x + 4) = 2x + 2(4)
![Page 6: 2.4 Reasoning with Properties from Algebra](https://reader033.vdocuments.net/reader033/viewer/2022061603/56813bf2550346895da5282b/html5/thumbnails/6.jpg)
Using the property of Algebra to solve an equation
3x + 12 = 8x – 18 Given
![Page 7: 2.4 Reasoning with Properties from Algebra](https://reader033.vdocuments.net/reader033/viewer/2022061603/56813bf2550346895da5282b/html5/thumbnails/7.jpg)
Using the property of Algebra to solve an equation
3x + 12 = 8x – 18 Given
- 3x = - 3x Reflexive Property
![Page 8: 2.4 Reasoning with Properties from Algebra](https://reader033.vdocuments.net/reader033/viewer/2022061603/56813bf2550346895da5282b/html5/thumbnails/8.jpg)
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
![Page 9: 2.4 Reasoning with Properties from Algebra](https://reader033.vdocuments.net/reader033/viewer/2022061603/56813bf2550346895da5282b/html5/thumbnails/9.jpg)
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
![Page 10: 2.4 Reasoning with Properties from Algebra](https://reader033.vdocuments.net/reader033/viewer/2022061603/56813bf2550346895da5282b/html5/thumbnails/10.jpg)
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
![Page 11: 2.4 Reasoning with Properties from Algebra](https://reader033.vdocuments.net/reader033/viewer/2022061603/56813bf2550346895da5282b/html5/thumbnails/11.jpg)
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
![Page 12: 2.4 Reasoning with Properties from Algebra](https://reader033.vdocuments.net/reader033/viewer/2022061603/56813bf2550346895da5282b/html5/thumbnails/12.jpg)
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
![Page 13: 2.4 Reasoning with Properties from Algebra](https://reader033.vdocuments.net/reader033/viewer/2022061603/56813bf2550346895da5282b/html5/thumbnails/13.jpg)
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
![Page 14: 2.4 Reasoning with Properties from Algebra](https://reader033.vdocuments.net/reader033/viewer/2022061603/56813bf2550346895da5282b/html5/thumbnails/14.jpg)
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
![Page 15: 2.4 Reasoning with Properties from Algebra](https://reader033.vdocuments.net/reader033/viewer/2022061603/56813bf2550346895da5282b/html5/thumbnails/15.jpg)
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
![Page 16: 2.4 Reasoning with Properties from Algebra](https://reader033.vdocuments.net/reader033/viewer/2022061603/56813bf2550346895da5282b/html5/thumbnails/16.jpg)
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
![Page 17: 2.4 Reasoning with Properties from Algebra](https://reader033.vdocuments.net/reader033/viewer/2022061603/56813bf2550346895da5282b/html5/thumbnails/17.jpg)
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
![Page 18: 2.4 Reasoning with Properties from Algebra](https://reader033.vdocuments.net/reader033/viewer/2022061603/56813bf2550346895da5282b/html5/thumbnails/18.jpg)
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
![Page 19: 2.4 Reasoning with Properties from Algebra](https://reader033.vdocuments.net/reader033/viewer/2022061603/56813bf2550346895da5282b/html5/thumbnails/19.jpg)
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
![Page 20: 2.4 Reasoning with Properties from Algebra](https://reader033.vdocuments.net/reader033/viewer/2022061603/56813bf2550346895da5282b/html5/thumbnails/20.jpg)
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
![Page 21: 2.4 Reasoning with Properties from Algebra](https://reader033.vdocuments.net/reader033/viewer/2022061603/56813bf2550346895da5282b/html5/thumbnails/21.jpg)
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
![Page 22: 2.4 Reasoning with Properties from Algebra](https://reader033.vdocuments.net/reader033/viewer/2022061603/56813bf2550346895da5282b/html5/thumbnails/22.jpg)
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.
![Page 23: 2.4 Reasoning with Properties from Algebra](https://reader033.vdocuments.net/reader033/viewer/2022061603/56813bf2550346895da5282b/html5/thumbnails/23.jpg)
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.
![Page 24: 2.4 Reasoning with Properties from Algebra](https://reader033.vdocuments.net/reader033/viewer/2022061603/56813bf2550346895da5282b/html5/thumbnails/24.jpg)
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.
![Page 25: 2.4 Reasoning with Properties from Algebra](https://reader033.vdocuments.net/reader033/viewer/2022061603/56813bf2550346895da5282b/html5/thumbnails/25.jpg)
Given Find
#1. #1. Given
18043
9321
180321
mm
mm
mmm
4m
18043
180321
mm
mmm
![Page 26: 2.4 Reasoning with Properties from Algebra](https://reader033.vdocuments.net/reader033/viewer/2022061603/56813bf2550346895da5282b/html5/thumbnails/26.jpg)
Given Find
#1. #1. Given
#2. #2. Subst. Prop
18043
9321
180321
mm
mm
mmm
4m
18043
180321
mm
mmm
43321 mmmmm
![Page 27: 2.4 Reasoning with Properties from Algebra](https://reader033.vdocuments.net/reader033/viewer/2022061603/56813bf2550346895da5282b/html5/thumbnails/27.jpg)
Given Find
#1. #1. Given
#2. #2. Subst. Prop
#3. #3. Reflex Prop.
18043
9321
180321
mm
mm
mmm
4m
18043
180321
mm
mmm
43321 mmmmm
33 mm
![Page 28: 2.4 Reasoning with Properties from Algebra](https://reader033.vdocuments.net/reader033/viewer/2022061603/56813bf2550346895da5282b/html5/thumbnails/28.jpg)
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
![Page 29: 2.4 Reasoning with Properties from Algebra](https://reader033.vdocuments.net/reader033/viewer/2022061603/56813bf2550346895da5282b/html5/thumbnails/29.jpg)
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
![Page 30: 2.4 Reasoning with Properties from Algebra](https://reader033.vdocuments.net/reader033/viewer/2022061603/56813bf2550346895da5282b/html5/thumbnails/30.jpg)
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
![Page 31: 2.4 Reasoning with Properties from Algebra](https://reader033.vdocuments.net/reader033/viewer/2022061603/56813bf2550346895da5282b/html5/thumbnails/31.jpg)
HomeworkHomework
Page 99 – 101 Page 99 – 101
# 10 - 25, 27, 32# 10 - 25, 27, 32