1. Algebraic proof
Chapter 2 Section 6

2. Properties of Equality2
Addition Property
If a = b, then a + c = b + c
Subtraction Property
If a = b, then a – c = b – c
Multiplication Property
If a = b, then a * c = b * c
Division Property
If a = b and c ≠ 0, then a/c = b/c
Reflexive Property
a = a
Symmetric Property
If a = b, then b = a
Transitive Property
If a = b and b = c, then a = c
Substitution Property
If a = b, then b can replace a in any expression
Distributive Property
a(b + c) = ab + ac

3. Solve and Write a Justification for Each Step3
Solve 6x + 2(x - 1) = 30 and write a justification for each step:
6x + 2(x - 1) = 30
6x + 2x - 2 = 30
8x - 2 = 30
8x = 32
8x = 32
x = 4
Given or original equation
Distributive Property
Combine Like Terms
Addition property
Division property of =
Simplify

4. This leads to “Proof Writing”

5. How to Set Up a 2-column Proof
Given:
Prove:
Statement Reason
Diagram

6. Write a geometric proof
Give a reason for each step
Multiplication
Distributive
Addition

7. Write a 2-column proof
Distributive
Subtraction
Division

8. Properties of Congruence
Reflexive Property
AB ≅ AB
∠ A ≅ ∠ A
Symmetric Property
If AB ≅ CD, then CD ≅ AB
If ∠ A ≅ ∠ B, then ∠ B ≅ ∠ A
Transitive Property
If AB ≅ CD and CD ≅ EF, then AB ≅ EF
If ∠ A ≅ ∠ B and ∠ B ≅ ∠ C,then ∠ A ≅ ∠ C

9. Using Properties of Equality and Congruence
State the property that justifies each statement
1.Reflexive
2.Division
3.Multiplication
4.subtraction
5.Substitution
6.Addition
7.Transitive 1. 2. 3. 4. 5. 6. 7.

10. Write a 2-column proof If DF EG, then x = 10 ≅ D E Statements Reasons11
1. DF = EG
2. 11 = 2x - 9
3. 20 = 2x
4. 10 = x
1. Given
2. Substitution
3. Addition
4. Division G F

11. Write a 2 –column proof 1. Given 1. <Y = <Z 2. Substitution
If <Y <Z, then x = 100 ≅
Statements
Reasons
1. <Y = <Z
2. x + 10 = 2x - 90
= x - 90
= x
1. Given
2. Substitution
3. Subtraction
4. Addition
X +10 y Z
2x- 90

12. Have a great day! 