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Review properties of equality and use them to write algebraic proofs. PowerPoint Presentation
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Review properties of equality and use them to write algebraic proofs. - PowerPoint PPT Presentation


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Objectives. Review properties of equality and use them to write algebraic proofs. A proof uses logic, definitions, properties, and previously proven statements to “prove” that a conclusion is true. An important part of writing a proof is giving justifications to show that every step is valid.

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Presentation Transcript
slide1

Objectives

Review properties of equality and use them to write algebraic proofs.

slide2

A proof uses logic, definitions, properties, and previously proven statements to “prove” that a conclusion is true.

  • An important part of writing a proof is giving justifications to show that every step is valid.
  • Possible ways to “prove” or justify each step:
  • A definition
  • A postulate
  • A property
  • Something given in the problem
slide4

Remember!

The Distributive Property states that

a(b + c) = ab + ac.

slide5

Example 1: Solving an Equation in Algebra

Solve the equation 4m – 8 = –12. Write a justification for each step.

4m – 8 = –12

+8+8

4m = –4

m = –1

slide6

Solve the equation . Write a justification for each step.

t = –14

Check It Out! Example 1

slide7

Helpful Hint

AB

AB represents the length AB, so you can think of AB as a variable representing a number.

Like algebra, geometry also uses numbers, variables, and operations. For example, segment lengths and angle measures are numbers. So you can use these same properties of equality to write algebraic proofs in geometry.

slide8

Example 2: Solving an Equation in Geometry

Write a justification for each step.

NO = NM + MO

4x – 4 = 2x + (3x – 9)

4x – 4 = 5x – 9

–4 = x – 9

5 = x

slide9

Check It Out! Example 2

Write a justification for each step.

mABC = mABD + mDBC

8x°=(3x + 5)°+ (6x – 16)°

8x = 9x – 11

–x = –11

x = 11

slide10

Check It Out! Example 2

Write a justification for each step.

mABC = mABD + mDBC

8x°=(3x + 5)°+ (6x – 16)°

8x = 9x – 11

–x = –11

x = 11

slide11

Classwork:

Exit Ticket with Partner

Homework:

  • 2.5 Practice B Homework Handout
    • Must write out justification for each step to get credit!!
slide12

Given

z – 5 = –12

Mult. Prop. of =

z = –7

Add. Prop. of =

Lesson Quiz: Part I

Solve each equation. Write a justification for each step.

1.

slide13

Given

z – 5 = –12

Mult. Prop. of =

z = –7

Add. Prop. of =

Lesson Quiz: Part I

Solve each equation. Write a justification for each step.

1.

slide14

Given

6r – 3 = –2(r + 1)

6r – 3 = –2r – 2

Distrib. Prop.

Add. Prop. of =

8r – 3 = –2

8r = 1

Add. Prop. of =

Div. Prop. of =

Lesson Quiz: Part II

Solve each equation. Write a justification for each step.

2.6r – 3 = –2(r + 1)

slide15

WARM UP

Give an example of the following properties:

1. Reflexive Property of Equality:

2. Symmetric Property of Equality:

3. Transitive Property of Equality:

slide16

Objective:

Identify properties of equality and congruence.

Remember…..segments with equal lengths are congruent and that angles with equal measures are congruent.

So the Reflexive, Symmetric, and Transitive Properties of Equality have corresponding properties of congruence.

slide18

Remember!

Numbers are equal (=) and figures are congruent ().

slide19

Example 1: Identifying Property of Equality and Congruence

Identify the property that justifies each statement.

A. QRS  QRS

B. m1 = m2 so m2 = m1

C. AB  CD and CD  EF, so AB EF.

D. 32° = 32°

Reflex. Prop. of .

Symm. Prop. of =

Trans. Prop of 

Reflex. Prop. of =

slide20

Check It Out! Example 2

Identify the property that justifies each statement.

A. DE = GH, so GH = DE.

B. 94° = 94°

C. 0 = a, and a = x. So 0 = x.

D. A  Y, so Y  A

Sym. Prop. of =

Reflex. Prop. of =

Trans. Prop. of =

Sym. Prop. of 

slide21

Lesson Review

Identify the property that justifies each statement.

1. x = y and y = z, so x = z.

2. DEF  DEF

3. ABCD, so CDAB.

Trans. Prop. of =

Reflex. Prop. of 

Sym. Prop. of 

slide22

Classwork/Homework

come up with a unique example of each