Stepp's Prentice Hall Geometry Chapter 2 Reasoning And Proof
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| conditional | another name for if, then statements
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| hypothesis | the part following "if"
also represented by "p"
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| Conclusion | the part following "then" represented by "q"
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| truth value | true or false
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| converse | statement obtained by switching p and q so that q implies p
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| biconditional | when a statement and its converse are both true they can be combined into one statement with "if and only if"
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| Good Definitions | are reversable
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| The arrow on a biconditional | points both ways
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| If the converse is false | you can not write a biconditional
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| the term conversely means the same as | vica versa
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| deductive reasoning | logically connecting given statements to the appropriate conclusions
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| Law of Detachment | if a conditional is true, then the conclusion is true any time you find the hypothesis
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| Law of Syllogism | if the conclusion of one statement is also the hypothesis of another statement then you can form a third conditional statement connecting the original hypothesis with the final conclusion
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| If p implies q and q implies r then | p implies r
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| If p imples q is a true statement and you found p to be true then | q must be true
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| If p implies q and you found q then | you know nothing
you can only make a conclusion when you are given p ( unless it was an "if and only if" statement)
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| iff means | if and only iff, you have a biconditional (both the statemtent AND its converse are true
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| Addition Property of EQUALITY | you can add the same quanity to both sides of an equation and the result is also true
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| Subtraction Property of EQUALITY | you can subtract the same quanity from both sides of an equation and the result is also true
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| Multiplication Property of EQUALITY | you can multiply both sides of an equation by the same quanity and the result is also true
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| Division Property of EQUALITY | you can divide both sides of an equation by the same quanity and the result is also true
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| Reflexive Property of EQUALITY | everything is equal to itself (you see your reflection in a mirror)
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| Symmetric Property of EQUALITY | if a = b then b=a
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| Transitive Property of EQUALITY | if two things are both equal to a third thing then they are also equal to each other
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| Substitution Property of EQUALITY | if a=b then you can replace a with b anywhere
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| The Distributive Property | a(b + c) = ab + ac
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| Properties of Congruence | Reflexive, Symmetric, and Transitive properties are not only good for equality (with numbers) they also work with congruence (figures)
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| THEOREM | A statement that you can prove to be true with deductive reasoning
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| Proof | the set of steps you take to show a conjecture is true
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| Paragraph Proof | written statements that are backed up by proper reasons to show a stateement is true
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| Two column proof | form with numberd statements and corresponding reasons for making those statements
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| Given | material or information that has been supplied to you. You assume it to be true because it was "GIVEN."
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| First reason in a two column proof | given
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| Angle Addition Postulate | part + part = whole angle
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| Last statement in a proof | the prove statement
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| You have to have 2 conditionals to use the | Law of Syllogism
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| Most common mistake using the Law of Detachment | assuming the converse is true
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| A statemen you can prove true is a | theorem
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| Vertical Angles | are opposite angles formed by two intersecting lines and they are CONGRUENT
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| How do you write the two conditionals that form a biconditional | first write the if, then statement, then write it's converse
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| checklist for angles | vertical, supplementary, complementary, angle addition postulate.
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