Download Algebraic Properties

Algebraic Properties
Algebraic properties of equality are
used in geometry. They help to solve
problems and provide justification for
each step.
Algebraic Properties
Reflexive Property
a=a
Symmetric Property If a = b,
then b = a.
Transitive Property If a = b and
b = c, then
a = c.
Addition Property If a = b,
then a + c = b + c
Subtraction Property
If a = b,
then a – c = b - c
Multiplication Property
If a  b,
then a  c  b  c
Division Property
If a  b,
a b
then  .
c c
Substitution Property
If a = b and a = c,
then b = c.
If a = b and
x = 2a + 4, then
x = 2b + 4.
Distributive Property
a(b + c) = ab + ac
Combine like terms – combine terms on
one side of an equation.
Reflexive, Symmetric, and
Transitive Properties have
corresponding properties of
congruence
Name the property that justifies each
statement.
b). mABC = mABC
Reflexive Property
9
e. If 2x = 9, then x = .
2
Division Property
b. If 12 = AB, then AB = 12.
Symmetric Property
d. If y = 75 and y = mA, then
mA = 75.
Substitution Property
c. If AB = BC, and BC = CD, then
AB = CD.
Transitive Property
1. Name the property that justifies each
statement.
a. If AB + BC = DE + BC, then AB = DE.
Subtraction Property
x
d. If  5, then x  15.
3
Multiplication Property
c. If XY = PQ and XY = RS, then
PQ = RS.
Substitution Property
2. Name the property that justifies each
statement.
a. If 3x = 120, then x = 40.
Division Property
3. What is the value of x? Justify each step.
(2x + 30)° x°
O
A
M
C
1. AOM and MOC are
supplementary
Angles that form a linear pair are
supplementary.
2. mAOM + mMOC =
180°
If two angles are supplementary,
they add to 180°.
(2x + 30) + x = 180°
Substitution Property
3x + 30 = 180°
3x = 150°
x = 50°
4. What is the value of x? Justify each step.
R
x°
Given: AB bisects RAN
AB bisects RAN
Given
A
B
(2x – 75)°
N
mRAB = mBAN
A bisector divides an angle into 2
congruent angles.
x = 2x – 75
Substitution Property
-x = -75
x = 75