Learning Goals
Use properties from algebra to solve algebraic
proofs
Use properties of length and measure to justify
segment and angle relationships.
ESLRs: Becoming Competent Learners, Complex Thinkers,
ESLRs: Becoming Competent Learners, Complex Thinkers, and
andEffective
Effective
Communicators
Communicators
Addition Property of Equality
If a  b, then a  c  b  c
Example: If x  6  8, then ( x  6)  6  8  6
Subtraction Property of Equality
If a  b, then a  c  b  c
Example: If x  2  5, then ( x  2)  2  5  2
Multiplication Property of Equality
If a  b, then ac  bc
Example: If
x
x
 12, then 3    12 3
3
3
Division Property of Equality
a b
If a  b, then

c c
Example: If 6x = 8, then 6x = 8
6
6
Reflexive Property
For any real number a, a  a
Symmetric Property
If a  b, then b  a
Example: If 9  x  4, then x  4  9
Transitive Property
If a  b and b  c, then a  c
Example: If x  4  9 and 9  27  y, then x  4  27  y
Substitution Property
If a = b, then a can be substituted for b
in any equation or expression.
Distributive Property
If a(b  c), then ab  ac
Identity Property (add these to your notes)
a0  a
a 1 a
Inverse Property (add these to your notes)
a  ( a )  0
a a 1  1 ( a  0)
Solve the equation and give a reason for each step.
3x  12  8x 18
3x  3x 12  8x  3x 18
0  12  8x  3x 18
0 12  5x 18
12  5x 18
12  18  5x 18  18
30  5x  0
30  5x

5
5
6  1x
6 x
x6
Given equation
Add Prop of Equality
Inverse Prop
Distributive Prop
Identity Prop
Add Prop of Equality
Inverse Prop
Identity Prop
Mult. Prop of Equality
Inverse Prop
Identity Prop
Symmetric Prop
AC = BD. Verify that AB = CD
A
1.
2.
3.
4.
5.
6.
7.
B
AC  BD
AC  AB  BC
BD  BC  CD
AB  BC  BC  CD
BC  BC
AB  BC  BC  BC  BC  CD
AB  0  0  CD
AB  CD
C
D
given
Segment Add. Post.
Substitution Prop
Reflexive Prop of =
Add/subtraction Prop of =
Inverse Prop
Identity Prop
In the diagram of a baseball diamond, the pitcher's
mound is at Ð3. Use the following information to
find mÐ4.
1.
m1  m2  m3  180
m1  m2  93
m3  m4  180
m1  m2  m3  180
m3  m4  180
2
4
3
90 ft 1
90 ft
given
4.
m1  m2  m3  m3  m4 Substitution/Transitive Prop.
Add/subtraction Prop of =
m1  m2  m4
given
m1  m2  93
5.
93  m4
2.
3.
Substitution/Transitive Prop
What purpose do the Properties of Equality
serve in mathematics?
Choose one of the properties and give a real
life example.
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