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Geometry Ch. 2
Geometric Reasoning- vocabulary
| Term | Definition |
|---|---|
| inductive reasoning | the process of reasoning that a rule or statement is true because specific cases are true |
| conjecture | a statement believed to be true based on inductive reasoning |
| counterexample | an example that proves a conjecture or statement is false |
| conditional statement (words) | "if p, then q" |
| hypothesis | the part p of a conditional statement following the word 'if' |
| conclusion | the part q of a conditional statement following the word 'then' |
| conditional statement (symbols) | p --> q |
| negation of p (symbols) | ~p |
| negation of p (words) | "not p" |
| converse (words) | the statement formed by exchanging the hypothesis and conclusion |
| converse (symbols) | q --> p |
| inverse (words) | the statement formed by negating the hypothesis and the conclusion |
| inverse (symbols) | ~p --> ~q |
| contrapositive (words) | the statement formed by exchanging AND negating the hypothesis and conclusion |
| contrapositive (symbols) | ~q --> ~p |
| logically equivalent statements | statements that have the same truth value |
| deductive reasoning | the process of using logic to draw conclussions |
| Law of Detachment | if p-->q is true and p is true, then q is true |
| Law of Syllogism | if p-->q and q-->r are true statements, then p-->r is a true statement |
| biconditional statement | a statement that can be in the form "p if and only if q" |
| definition | a statement that describes a mathematical object and can be written as a true biconditional statement. |
| 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 |
| quadrilateral | a four sided polygon |
| triangle | a three sided polygon |
| proof | an argument that uses logic to show that a conclusion is true |
| Addition Property of Equality | If a = b, then a + c = b + c. |
| Subtraction Property of Equality | If a = b, then a - c = b - c. |
| Multiplication Property of Equality | If a = b, then ac = bc. |
| Division Property of Equality | If a = b, then a/c = b/c. |
| Reflexive Property of Equality | a = a |
| Symmetric Property of Equality | If a = b, then b = a. |
| Transitive Property of Equality | If a = b and b = c, then a = c. |
| Substitution Property of Equality | If a = b, then b can be substituted for a in any expression. |
| Distributive Property | a(b + c) = ab + ac |
| Reflexive Property of Congruence | figure A ≅ figure A |
| Symmetric Property of Congruence | If figure A ≅ figure B, then figure B ≅ figure A. |
| Transitive Property of Congruence | If figure A ≅ figure B and figure B ≅ figure C, then figure A ≅ figure C. |
| theorem | a statement that has been proven |
| 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 |
| flowchart proof | a style of proof that uses boxes and arrows to show the structure of the proof |
| paragraph proof | a style of proof in which the statements and reasons are presented in paragraph form |
Created by:
rismith
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