Algebraic Proofs and Properties

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