Download Geometry: Week 1.4 Day 1

Notes: ALGEBRAIC PROPERTIES
Content Objective: I will be able to use algebraic properties to prove logical
arguments.
PROPERTIES OF EQUALITY
PROPERTY
ALGEBRAIC EXAMPLE
EXAMPLE
Addition Property
If a = b, then a + c = b + c
If x-3 = 6, then x = __________
Subtraction Property
If a = b, then a – c = b - c
If 2x +12 =20, then 2x = _______
Multiplication
Property
If a = b, then a · c = b ·c
If
Division Property
If a = b, then
a b

c c
x
 2 , then x = ___________
4
If -6x = 20 , then x =________
PROPERTY
ALGEBRAIC EXAMPLE
EXAMPLE
Reflexive Property
a=a
3 = ____________
Symmetric Property
If a = b, then b = a
If 3 = x, then _______
Transitive Property
If a = b, b = c, then a = c
If 2 = x, x = a, then ________
Distributive Property
a(b + c) = ___________________
Substitution Property
If x = 3 and x + 8, ________________
Geometry Unit 1 - Essentials of Geometry
Page 1
Notes: Algebraic Properties
EXAMPLE 1: Use the property to complete each statement.
1. Addition Property of Equality: If AB = XY, then AB + 15 = XY _________ .
2. Distributive Property of Equality: 3(2x – 1) = ________.
QUICK CHECK:
3. Symmetric Property of Equality: If 3 = x, then
4. Transitive Property of Equality: If mA = mB and mB = mC, then
5. Substitution Property of Equality: If XY = 2, then RM + XY = RM +
EXAMPLE 2: Solve the following equation and give a reason for each step
4x – 8 = 90
Statements
Reasons
4x – 8 = 90
Given.
4x – 8 + 8 = 90 + 8
4x = 98
Simplify by combining like terms.
4 x 98

4
4
x = 24.5
Geometry Unit 1 - Essentials of Geometry
Simplify.
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Notes: Algebraic Properties
EXAMPLE 3: The following equation has been solved, justify each step.
-2(3x – 1) = 180
Statements
Reasons
-2(3x – 1) =180
-6x + 2 = 180
-6x + 2 - 2 = 180 - 2
Addition Property of Equality
-6x = 178
Simplify.
 6 x 178

6
6
x =  29
2
3
Simplify.
QUICK CHECK: The following equation has been solved, justify each step.
3x – 5 = 90
Statements
3x – 5 = 90
Reasons
Given
3x – 5 + 5 = 90 + 5
3x = 95
Simplify by combining like terms.
3 x 95

3
3
x
95
3
Geometry Unit 1 - Essentials of Geometry
Simplify by combining like terms.
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Notes: Algebraic Properties
EXAMPLE 4: The following equation has been solved, justify each step.
8x + 4(2+x) = 180
Statements
Reasons
8x  8  4x  180
12x  8  180
12x  8  8  180  8
12 x  172
12 x 172

12
12
x  14
1
3
QUICK CHECK: Solve the following equation. Justify each step.
1
x  5  90
2
Statements
Geometry Unit 1 - Essentials of Geometry
Reasons
Page 4