Download Algebraic proof

Algebraic proof
Chapter 2 Section 6
Properties of Equality
2
Addition Property
If a = b, then a + c = b + c
If a = b, then a – c = b – c
Subtraction Property
Multiplication Property If a = b, then a * c = b * c
If a = b and c ≠ 0, then a/c =
Division Property
Reflexive Property
Symmetric Property
Transitive Property
Substitution Property
Distributive Property
b/c
a=a
If a = b, then b = a
If a = b and b = c, then a = c
If a = b, then b can replace a
in any expression
a(b + c) = ab + ac
3
Solve and Write a Justification
for Each Step
Solve 6x + 2(x - 1) = 30 and write a
justification for each step:
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


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6x + 2(x - 1) = 30
6x + 2x - 2 = 30
8x - 2 = 30
8x = 32
8x = 32
8
8
x=4
Given or original equation
Distributive Property
Combine Like Terms
Addition property
Division property of =
Simplify
This leads to “Proof Writing”
How to Set Up a 2-column Proof

Given:

Prove:
Diagram


Statement
Reason
Write a geometric proof
Give a reason for each step
Multiplication
Distributive
Addition
Write a 2-column proof
Distributive
Subtraction
Division
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
Using Properties of Equality
and Congruence
State the property that justifies each statement
1.Reflexive
1.
2.
3.
4.
5.
6.
7.
2.Division
3.Multiplication
4.subtraction
5.Substitution
6.Addition
7.Transitive
Write a 2-column proof
If DF ≅
D
11
F
EG, then x = 10
E
2x - 9
G
Statements
1. DF = EG
2. 11 = 2x - 9
3. 20 = 2x
4. 10 = x
Reasons
1. Given
2. Substitution
3. Addition
4. Division
Write a 2 –column proof
If <Y ≅<Z, then x = 100
Statements
X +10
y
Z
2x- 90
1. <Y = <Z
2. x + 10 = 2x - 90
3. 10 = x - 90
4. 100 = x
Reasons
1. Given
2. Substitution
3. Subtraction
4. Addition
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