Transcript Using Properties from Algebra to Prove Statements

Using Properties from Algebra to
Prove Statements
Section 2.5
Essential Question
• How are algebraic properties used in logical
arguments?
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Add 18 to your birth month
Multiply by 25
Subtract 333
Multiply by 8
Subtract 554
Divide by 2
Add your birth date
Multiply by 5
Add 692
Multiply by 20
Add only the last two digits of your birth year
Subtract 32940 to get your birthday!
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Multiply the first number of your age by 5.
Add 3.
Double this figure.
Add the second number your age to the figure
Deduct 6 and you will have their age.
• Whenever you solve for a variable you are
unknowingly using different algebraic
properties.
• The algebraic properties that we will look at are:
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Addition Property
Subtraction Property
Multiplication Property
Division Property
Substitution Property
Distributive Property
Reflexive Property
Symmetric Property
Transitive Property
Let’s try one
• 2x – 5 = x + 12
Given
• 2x = x + 17
Addition Property
• X = 17
Subtraction Property
How ‘bout another
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Using the properties to prove
statements
• Algebraic proofs require you to solve the
problem algebraically and then state the
property that allows you to do each step.
• Proofs that are more geometric require you to do
the same thing, but are slightly more abstract.
Proving two angles are supplementary.
• Angle ABC and CBD are a linear pair
• m ABC + m CBD = 180°
Given
Def. Linear
Pair
• Angle ABC and CBD are supplementary Def.
Supplementary
Show that the areas are the same.
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