Geometric Reasoning- vocabulary
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| inductive reasoning | the process of reasoning that a rule or statement is true because specific cases are true
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| conjecture | a statement believed to be true based on inductive reasoning
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| counterexample | an example that proves a conjecture or statement is false
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| conditional statement (words) | "if p, then q"
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| hypothesis | the part p of a conditional statement following the word 'if'
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| conclusion | the part q of a conditional statement following the word 'then'
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| conditional statement (symbols) | p --> q
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| negation of p (symbols) | ~p
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| negation of p (words) | "not p"
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| converse (words) | the statement formed by exchanging the hypothesis and conclusion
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| converse (symbols) | q --> p
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| inverse (words) | the statement formed by negating the hypothesis and the conclusion
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| inverse (symbols) | ~p --> ~q
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| contrapositive (words) | the statement formed by exchanging AND negating the hypothesis and conclusion
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| contrapositive (symbols) | ~q --> ~p
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| logically equivalent statements | statements that have the same truth value
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| deductive reasoning | the process of using logic to draw conclussions
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| Law of Detachment | if p-->q is true and p is true, then q is true
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| Law of Syllogism | if p-->q and q-->r are true statements, then p-->r is a true statement
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| biconditional statement | a statement that can be in the form "p if and only if q"
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| definition | a statement that describes a mathematical object and can be written as a true biconditional statement.
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| polygon | a closed plane figure formed by three or more segments such that each segment intersects exactly two other segments only at their endpoints and no two segments with a common endpoint are collinear
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| quadrilateral | a four sided polygon
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| triangle | a three sided polygon
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| proof | an argument that uses logic to show that a conclusion is true
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| Addition Property of Equality | If a = b, then a + c = b + c.
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| Subtraction Property of Equality | If a = b, then a - c = b - c.
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| Multiplication Property of Equality | If a = b, then ac = bc.
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| Division Property of Equality | If a = b, then a/c = b/c.
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| Reflexive Property of Equality | a = a
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| Symmetric Property of Equality | If a = b, then b = a.
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| Transitive Property of Equality | If a = b and b = c, then a = c.
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| Substitution Property of Equality | If a = b, then b can be substituted for a in any expression.
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| Distributive Property | a(b + c) = ab + ac
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| Reflexive Property of Congruence | figure A ≅ figure A
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| Symmetric Property of Congruence | If figure A ≅ figure B, then figure B ≅ figure A.
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| Transitive Property of Congruence | If figure A ≅ figure B and figure B ≅ figure C, then figure A ≅ figure C.
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| theorem | a statement that has been proven
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| two-column proof | a style of proof in which the statements are written in the left-hand column and the reasons are written in the right-hand column
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| flowchart proof | a style of proof that uses boxes and arrows to show the structure of the proof
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| paragraph proof | a style of proof in which the statements and reasons are presented in paragraph form
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Created by:
rismith
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