1. a + c = b + c
a - c = b - c
ac = bc a c b =
a can be
substituted for b in any
equation or expression

2. 2x + 3 = 9 - x
+x x x
Addition Property of Equality
___________
3x + 3 = 9
_________
3x = 6
Subtraction Property of Equality 3
3x = 6 3
x = 2 2
Division Property of Equality

3. ab + ac
-24x - 8
Distributive Property of Equality
-24x
Addition x
Division
-24

4. x - 5 = 7 + 2x Given
-5 = 7 + x Subtraction Property of Equality
-12 = x Subtraction Property of Equality
4(5 - x) = -2x Given
20 - 4x = -2x Distributive Property of Equality
20 = 2x Addition Property of Equality
10 = x Division Property of Equality

5. 3.5s
Distributive Property s
17.5
Addition
17.5
3.5
Division d +
= s or

6. a = a
AB = AB
m∠A = m∠A
KT = KT because it's the same length in both triangles
b = a
CD = AB
m∠B = m∠A
The Symmetric Property is pretty straightforward but it isn't used too often.
a = c
AB = EF
m∠A = m∠C
The Transitive Property is similar to the Law of Syllogism because the output of one statement is the input of another.
These properties are regularly used as reasons in Two-Column proofs.

7. This is really an example of a Two-Column proof
This is really an example of a Two-Column proof. The column on the left are Statements and the column on the right are Reasons. EF
(it's given info b/c of the congruence symbols) DE
Segment Addition Postulate
DE EF
Substitution AC
Transitive AC
Addition
CF AD

8. d = 5(s + 3) Given d 5
= s + 3
Division Property
- 3 = s
Subtraction Property
d = 5s Distributive Property
d - 15 = 5s Subtraction Property - 15
= s
Simplify OR
Symmetric Property of Equality
Transitive Property of Equality
Reflexive Property of Equality