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Notes- Algebraic proofs.notebook
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October 09, 2013
Topic: Algebraic ProofsEssential Questions: What are the 6 types of proofs that are used in Geometry?
Pick up the handouts from the back tableGet out your homework to be gradedFill out your assignment sheetBegin working on your warm-up
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October 09, 2013
Warm-up
Given the conditional statement, answer the following questions.
" If you are in a member of the orchestra, then you are a musician"
1) What is the hypothesis? _______________________2) What is the conclusion? _______________________3) What is the conditionals truth value? _____________ If false, provide acounterexample. _____________________________________________4) Write the converse of the given conditional? __________________________________________________________________5) What is the converse's truth value? If false, provide a counterexample? __________________________________________________________
Determine whether the following can be written as a biconditional. If so, write it in biconditional form.
"If two angles are congruent, then they have equal measures"
6) Is it a biconditional? _______________________
7) If yes, write it in biconditional form.
__________________________________________________________________
8) What type of geometric conditionals are always biconditionals? _____________
If possible, draw a conclusion from the given information and conditional statement
Given: <5 and <7 are complementaryConditional: If two angle are complimentary, then the sum of their measures is 90 degrees.
Conclusion: ____________________________________________________
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October 09, 2013
Answers to Homework
Converse: If an event is unlikely to occur, then the probability of the event is 0.1FalseCounterexample: The probability could be .005
Converse: If the air temperature is 320 F or less, then freezing rain is falling.False: May not be raining, could be snowing, etc.
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Homework Answers: Continued
17) T
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What is a proof?
An argument that uses logic, geometry conditionals, algebraic propertiesand previously proven statements to show that a conclusion is true.
There are 6 different types of proofs that are used in Geometry.
1) ____________________
2) ____________________
3) ____________________
4) ____________________
5) ____________________
6) _____________________
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October 09, 2013
An Algebraic Proof
Is used to justify why the conclusion (solution) to a particular algebraic problem is correct.Utilitizes Algebraic Properties as reason for each step in solving an equationIs set up in two-column format like Geometric 2-column proofs are set up
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October 09, 2013
Properties of AlgebraFill in your tables along with me
*** ADD IN MARGIN***
On pgs. 3-5 of your tables
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Guided Practice Problems
ex. 6 If 5=x, then x=5
ex. 7 If 1/3x=4, then x=12
ex. 8 If AB=2x and AB=CD, then
CD=2x.
Ex. 9 If 2AB=2CD, then
AB=CD.
List the property illustrated
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October 09, 2013
Two column proofs in Geometry
Two column proofs have 5 essential elements.
1) Given information
2) Conclusion to Prove
3) Diagram
4) Statements
5) Reasons
a) Postulatesb) Theoremsc) Corollariesd) Definitionse) Algebraic Properties
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October 09, 2013
2 column Proof template
1) Given
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October 09, 2013
1) Given
Example:
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October 09, 2013
Algebraic Two column proofs are set up the same way except...
They don't usually have a diagramThe reasons for your statements are the given and algebraic properties only
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October 09, 2013
Algebraic 2 column proof
2x-3=2/3
Prove: x = 11/6
Statement Reasons
1. 2x-3=2/3
2. 3(2x-3) = 2
3. 6x-9=2
* usually nodiagram is given
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ReasonsStatement
x/3 + 4 = 1
Prove: x = -9
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October 09, 2013
HomeworkW.S. Using Proofs in Algebra# 1-21 all
Finish conditional statementssheet
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October 09, 2013
