Logic: Algebraic Properties of Equality and Proofs

What's the Definition?

100

IF A=B, then B=A

What is the Symmetric Property?

200

If A=B, then AxC=BxC

What is the Multiplication Property? 

300

If A(B+C), then AB + AC

What is the Distributive Property?

400

If A=A, then A=A

What is the Reflexive Property?

500

If A=B and B=C, then A=C

What is the Transitive Property?

Name the Example

100

5x - 7 = 28

5x = 35 

What is the Addition Property?

200

12 = x 

x = 12 

What is the Symmetric Property?

300

24 = 2x

12 = x

What is the division property?

400

3w + d = 22

w = 2

6 + d = 22

What is the substitution property?

500

WV = DE

WV = 15 

DE = 15 

What is the Transitive Property?

Logic?

100

1, 2, 3, 4, ... The next two numbers are...

What is 5 and 6?

200

Describe the pattern below: 3, 5, 7, 9, 11, 13, 15,

What is the next consecutive odd number?

300

What are the next two numbers in the sequence? 1, 1, 2, 3, 5, ...

What is 8 and 13? 

400

What is the next number in the sequence? 1, -2, 3, -4, 5, -6, ...

What is 7? 

500

Describe the following pattern. 1, 4, 9, 16, 25, 36, 49, 64, ...

What is the next perfect square? 

Solving Proofs

100

Given: 4n - 2n = 4 Prove that n = 2

1. 4n - 2n = 4 1. Given 

2. 2n = 4 2. Combine Like Terms or Simplify 

3. n = 2 Division Property

200

Given: 7x - 9 = 54 Prove: x = 9 

1. 7x - 9 = 54 1. Given 

2. 7x = 63 2. Addition Property 

3. x = 9 Division Property 

300

Given: 4x - 12 = 20 Prove x = 8 

1. 4x - 12 = 20 1. Given 

2. 4x = 32 2. Addition Property 

3. x = 8 3. Division Property 

400

Given: x = 14 and 3w - x = 58 Prove w = 24 

1. x = 14 1. Given 

2. 3w - x = 58 2. Given 

3. 3w - 14 = 58 3. Substitution Property 

4. 3w = 72 4. Addition Property 

5. w = 24 5. Division Property 

500

Given: 4(3x+12)=2x-28 Prove: x = 7.6

Statements:

1)4(3x+12)=2x-28, 1. Given 

2)12x+48=2x-28, 2. Distributive Property

3)10x=-76,  Subtraction Property

4)x=-7.6 Division Property

 

Make Corrections

100

Every proof should start with what you are trying to prove. 

What is it should start with the given?

200

What are the next steps in this equation? 

1. 12w-4w=6. 1. Given 

2. 8w=6. 2. Combine Like Terms 

3. ? 3. ?

3. w=3/4.        3. Division property of equality

300

What is the reason for the statement?

1. 3x - 8 = 19  1. 

What is given?

400

Give the three reasons for each of the statements. 

1. 3x - 8 = 19  1. 

2. 3x = 27  2. 

3. x = 9      3. 

What is given, addition property, and division property? 

500

Angle A is congruent to Angle B 

Angle B is congruent to Angle C 

What other two angles are congruent?

What is Angle A = Angle C?