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Download Using Properties from Algebra to Prove Statements
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Using Properties from Algebra to Prove Statements Section 2.5 Essential Question • How are algebraic properties used in logical arguments? • • • • • • • • • • • • 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! • • • • • 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: ▫ ▫ ▫ ▫ ▫ ▫ ▫ ▫ ▫ 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 Page 108 #3 - 14 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. Page 109 # 26 - 29
