Algebraic Proofs and Properties

Presentation

•

Mathematics

•

9th Grade

•

Hard

Joseph Anderson

FREE Resource

13 Slides • 30 Questions

Algebra 1: Algebraic Properties

Copy this onto your Unit 2 notes page.

Copy this onto Algebraic Properties in your unit 2 notes.

Your unit 2 notes should include these properties.

Multiple Choice

For any numbers a, b, and c, if a = b and b = c, then a = c.

Transitive Property of Equality

Symmetric Property of Equality

Reflexive Property of Equality

Substitution Property of Equality

Multiple Choice

Identify the property of equality.
If 9=x, then x=9

Reflexive

Symmetric

Transitive

Substitution

Multiple Choice

What is the justification?

Vertical Angles Theorem

Transitive Property of Equality

Compliment Theorem

Reflexive Property of Congruence

Multiple Choice

What is the justification?

Segment Addition Postulate

Definition of Midpoint

Addition Property of Equality

Complement Theorem

Multiple Choice

What is the justification?

Transitive Property of Equality

Subtraction Property of Equality

Division Property of Equality

Substitution Property of Equality

Multiple Choice

If 3x + y = 14 and y = 9, then 3x + 9 = 14.

Reflexive Property of Equality

Symmetric Property of Equality

Transitive Property of Equality

Substitution Property of Equality

Multiple Choice

If ∠CAT is a right angle, then m∠CAT = 90°.

Definition of Right Angle

Definition of Congruent Angles

Angle Addition Postulate

Segment Addition Postulate

Multiple Choice

Identify the property shown.

Associative Property of Addition

Commutative Property of Addition

Distributive Property

Multiplication Property of 1

Multiple Choice

Identify the property shown.

Distributive Property

Commutative Property of Addition

Associative Property of Addition

Addition Property of 0

Multiple Choice

Which property is being used above?

Addition Property of Equality

Multiplication Property of Equality

Subtraction Property of Equality

Division Property of Equality

Multiple Choice

Name that property

Reflexive Property of Congruence

Transitive Property of Congruence

Symmetric Property of Congruence

Substitution Property of Equality

Multiple Choice

Which demonstrates the identity property of multiplication?

$0+5=5$

$8\cdot\left(-8\right)=-64$

$1\cdot6=6$

$0\cdot7=7$

Multiple Select

Which demonstrates the commutative property? Select all that apply.

$8+9=9+8$

$\left(4\cdot2\right)3=3\left(4\cdot2\right)$

$9-4=4-9$

$2\cdot3\cdot5=2\cdot5\cdot3$

$8\div4=4\div8$

Multiple Choice

Identify the property of equality used here:

39=39

Reflexive

Symmetric

Transitive

Substitution

Multiple Choice

$\left(4\cdot6\right)\cdot5=4\cdot\left(5\cdot6\right)$ represents what property?

Commutative property of multiplication

identity property of multiplication

associative property of multiplication

zero property of multiplication

Multiple Choice

What property? $5+\left(9+8\right)=\left(5+9\right)+8$

Commutative

Associative

Identity

Multiple Choice

Which property is represented below?
15(1) = 15

Identity

Commutative

Associative

Inverse

Multiple Choice

Complete the equation using the distributive property.

12x + 10 =

10 + 12x

12 + 10x

12(x+10)

2(6x + 5)

Multiple Choice

Determine which choice best shows the commutative property of multiplication.

1x1=1

(1x7)+(1x6)=

1x7=7x1

(1x7)x6=1x(7x6)

Multiple Choice

According to the Associative Property of Multiplication, (9 x 6) x 5 =

270

9 x 30

9 x (6 x 5)

5 x 9 + 5 x 6

Multiple Choice

True/False: $w+0=w$

True

False

Multiple Choice

true/false: $m-z=z-m\$ for all numbers m and z.

true

false

What does it mean to Justify Solutions to Linear Equations?

Using real number properties(such as the commutative, associative, and distributive properties) and the properties of equality (such as adding, subtracting, multiplying and dividing by a non-zero) to justify why each step in the process of solving a linear equation is legal!

To Justify means to...

Explain reasoning
Show Steps
Because we are justifying steps already taken, we will need to explain
Note:
APOE= Additive Property of Equality
MPOE= Multiplication Property of Equality

Multiple Select

What are examples of Justification in Algebra?

Explain the steps taken to solve with using real number properties and properties of equality

Show work AND Explain Steps taken using real number properties and properties of equality

Show all of your work ONLY

Let's Practice our new Justification Skills together!

Multiple Choice

Which property of real numbers justifies the work shown from Step 1 to Step 2?

Distributive Property

Commutative Property

Identity Property

Associative Property

Multiple Choice

Which property justifies the work shown?

Multiplication Property of Equality

Subtraction Property of Equality

Division Property of Equality

Multiplicative Inverse Property

Multiple Choice

Which property was used to get from Step 7 to the solution?

Distributive Property

Subtraction Property of Equality

Division Property of Equality

Substitution Property

Multiple Choice

Which property of real numbers justifies the work shown?

Distributive Property

Commutative Property

Identity Property

Associative Property

Multiple Choice

Which property justifies the work in solving this equation?

Addition Property of Equality

Additive Inverse Property

Identity Property of Addition

Subtraction Property of Equality

Multiple Choice

Which property of real numbers was used to get from Step 3 to Step 4?

Addition Property of Equality

Subtraction Property of Equality

Additive Inverse Property

Substitution Property

Multiple Choice

What is usually the 1st statement in reason column of a proof?

Prove

Given

Reason

Statement

Algebra 1: Algebraic Properties

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