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

18043

9321

180321

mm

mm

mmm

4m

18043

180321

mm

mmm

Given Find

#1. #1. Given

#2. #2. Subst. Prop

18043

9321

180321

mm

mm

mmm

4m

18043

180321

mm

mmm

43321 mmmmm

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

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

HomeworkHomework

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