Download Properties of Identity and Equality

2.4 Objective:
The student will be able to:
recognize and use algebraic
properties
Addition and Subtraction
Properties
1) Addition Property
For all numbers a, b and c if a = b, then:
a+c=b+c
2) Subtraction Property
For all numbers a, b and c if a = b, then:
a - c= b - c
Algebraic Properties
1)Reflexive Property:
For every number a,
a = a,
2) Symmetric Property:
For all numbers a and b, if a = b, then
a = b and b = a
If 4 = 2 + 2 then 2 + 2 = 4.
Multiplication Property:
For all numbers a, b and c if a = b, then:
a • c= b • c
Division Property:
For all numbers a, b and c if a = b and
if c ≠ 0, then:
More Properties
3) Transitive:
If a = b and b = c, then a = c.
If 4 = 2 + 2 and 2 + 2 = 3 + 1 then 4 = 3 + 1.
4) Substitution: If a = b, then a can be
replaced by b.
(5 + 2)x = 7x
The Distributive Property
The process of distributing the number
on the outside of the parentheses to
each term on the inside.
a(b + c) = ab + ac and (b + c) a = ba + ca
a(b - c) = ab - ac and (b - c) a = ba - ca
Example #1
5(x + 7)
5•x+5•7
5x + 35
Name the Property
1. If 2x+1= 4, then 2x = 3
Substraction
2. (10 + 2)  3 = 12  3
Substitution
3. 2 + 3 = 5 then 5 = 2 + 3
Symmetric
4. If 5  2 = 10 & 10 = 5 + 5 then
52=5+5
Transitive
5. If 7x = 21, then x = 3
Division Property
6. 2( 5+x) = 2• 5 +2 • x
Distributive
7. k + 7 = k + 7
Reflexive
8. 2+k = k+ 2
Symmetric
Example 1: Writing Reasons
Solve 5x – 18 = 3x +2
1. 5x – 18 = 3x + 2
1. Given
2. Subtraction property
2. 2x – 18 = 2
3. Addition property
3. 2x = 20
4. Division property
4. x = 10
Example 2: Writing Reasons
Solve 55z – 3(9z + 12)= -64
1. 55z – 3(9z + 12)= -64
2. 55z – 27z – 36 = -64
3. 28z – 36 = -64
4. 28z = -28
5. z = -1
1.
2.
3.
4.
5.
Given
Distributive property
Simplify
Addition property
Division property
Example 4: Using properties of length
1. AB = CD
1. Given
2.
3.
4.
5.
2.
3.
AB + BC = BC + CD
AC = AB + BC
BD = BC + CD
AC = BD
4.
5.
Addition property
Segment addition
postulate
Segment addition
postulate
Substitution property