Part 1:
Identify the algebraic properties of equality that are represented.
1.
Given
If [tex]a=b[/tex], then [tex]a\cdot c=b\cdot c, c\neq0[/tex]
The algebraic property of equality that is represented by the above expression is the multiplication property.
2.
Given
If [tex]a=b[/tex], then [tex]a- c=b- c,[/tex]
The algebraic property of equality that is represented by the above expression is the subtraction property.
3.
Given
If a = b, then a can be substituted for b (or b for a) in any equation or expression.
The algebraic property of equality that is represented by the above expression is the substitution property.
4.
Given
If [tex]a=b[/tex], then [tex] \frac{a}{c} = \frac{b}{c},\ c\neq0[/tex].
The algebraic property of equality that is represented by the above expression is the division property.
5.
Given
If [tex]a=b[/tex], then [tex]a+ c=b+ c,[/tex]
The algebraic property of equality that is represented by the above expression is the addition property.
6.
Given
sum: [tex]a(b+c)=ab+ac[/tex],
difference: [tex]a(b-c)=ab-ac[/tex]
The algebraic property of equality that is represented by the above expression is the distributive property.
7.
Given
If a = b and b = c, then a = c. If AB = CD and CD = EF, then AB = EF. If m<A = m<B and m<B = m<C, then m<A = m<C.
The algebraic property of equality that are represented by the above expression is the transitive property.
8.
Given
If a = b, then b = a. If AB = CD, then CD = AB. If m<A = m<B, then m<B = m<A.
The algebraic property of equality that are represented by the above expression is the symmetric property.
9.
Given
a = a, AB = AB, m<A = m<A
The algebraic property of equality that are represented by the above expression is the refrexive property.
10.
Given
If x = y, then 6x = 6y.
The algebraic property of equality that are represented by the above expression is the
multiplication property.
11.
Given
If AB = BC, then AB - 2 = BC - 2.
The algebraic property of equality that are represented by the above expression is the
subtraction property.
12.
Given
m<A = m<A
The algebraic property of equality that are represented by the above expression is the
refrexive property.
13.
Given
If AB = CD and CD = 6, then AB = 6
The algebraic property of equality that are represented by the above expression is the
transitive property.
14.
Given
If a = b, then b = a.
The algebraic property of equality that are represented by the above expression is the
symmetric property.
