Download 2.4Algebraic-Reasoning

Reasoning with
Properties of Algebra
proofs
Standards/Objectives:
Standard 3: Students will learn and apply
geometric concepts.
Objectives:
Use properties from Algebra
• Use properties of length and measure to
justify segment and angle relationships,
such as the angles at the turns of a
racetrack.
Algebraic properties
A few properties:
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–
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Addition property
Subtraction property
Multiplication property
Division property
Reflexive property
Symmetric property
Transitive property
Substitution property
Distributive Property
• a (b + c) = ab + ac
• Can be used to solve equations
• Example:
x + 3 = 7 By subtracting 3 from each side of
the equation, you obtain 4.
Example 1: Writing Reasons
Solve 5x – 18 = 3x +2
1. 5x – 18 = 3x + 2
2. 2x – 18 = 2
3. 2x = 20
4. x = 10
1. Given
2.
3.
4.
Subtraction property
Addition property
Division property
Example 2: Writing Reasons
•
Solve 55z – 3(9z + 12)= -64
1.
2.
3.
4.
5.
55z – 3(9z + 12)= -64
55z – 27z – 36 = -64
28z – 36 = -64
28z = -28
z = -1
1.
2.
3.
4.
5.
Given
Distributiveproperty
Simplify
Addition property
Division property
Example 4: Using properties of length
1. AB = CD
1. Given
2.
3.
4.
5.
2.
3.
AB + BC = BC + CD
AC = AB + BC
BD = BC + CD
AC = BD
4.
5.
Addition property
Segment addition
postulate
Segment addition
postulate
Substitution property
Example 5: Using properties of
measure
1.
2.
3.
4.
5.
6.
7.
m1 + m  2 = 66
m  1 + m  2+m  3 = 99 
66  + m  3 = 99
m  3 = 33 
m  3 = m  1, m  1 = m 
4
m3=m4
m  4 = 33 
1.
2.
3.
4.
5.
6.
7.
Given
Given
Substitution
Subtraction
Given
Transitive
Substitution