click below
click below
Normal Size Small Size show me how
H Geom chap 2 vocab
| Term | Definition |
|---|---|
| inductive reasoning | process of reasoning that a rule or statement is true because specific cases are true---when examples form a pattern and you assume the pattern will continue |
| conjecture | statement you believe to be true based on inductive reasoning--you MUST prove to show always true--find one example which is false to show not true |
| counterexample | the example given to show that a conjecture is not true |
| conditional statement | "if p, then q" |
| hypothesis | part p of a conditional statement-after the word if |
| conclusion | part q of a conditional statement-after the word then |
| truth value | validity of a conditional statement--either true (T) or false (F) |
| negation | use the word "not" to mean the opposite of a statement p looks like ~p |
| converse | reverse p and q in conditional statement "if q, then p" |
| inverse | negation of conditional statement "if ~p, then ~q" |
| contrapositive | reverse and negation of a conditional statement |
| logically equivalent statements | related conditional statements that have the same truth value |
| deductive reasoning | process of using logic to draw conclusions from given facts, definitions, and properties |
| biconditional statement | statement that can be written in the form "p if and only if q"-----means "if p, then q" and "if q, then p" |
| definition | statement that describes a mathematical object and can be written as a true biconditional |
| polygon | defined as a closed plane figure formed by 3 or more line segments |
| triangle | 3-sided polygon |
| quadrilateral | 4-sided polygon |
| proof | an argument that uses logic, definitions, properties, and previously proved statements to show that a conclusion is true |
| theorem | any statement that you can prove---once proven, can be used as a reason in later proofs |
| 2-column proof | reasons given in a logical order to verify a conclusion----start with given statements, then list reasons to find conclusions |
| flowchart proof | use boxes and arrows to show the structure of the proof |
| paragraph proof | style of proof that presents the steps of the proof and their matching reasons as sentences in a paragraph |