Geometry Vocabulary for Chapter 2

axiom

a statement that describes a fundamental relationship between the basic term of geometry

biconditional

the conjunction of a conditional statement and its convers

compound statement

a statement formed by joining two or more elements

conclusion

in a conditional statement, the statement that immediately follows the word "then

conditional statement

a statement that can be written in "if-then" form

conjecture

a educated guess based on known information

conjunction

a compound statement formed by joining two or more statements with the word "and

contrapositive

the statement formed by negating both the hypothesis and conclusion of a conditional statement

converse

the statement formed by exchanging the hypothesis and conclusion of a conditional statement

counter example

an example used to show that a given statement is not always true

deductive argument

a proof formed by a group of algebraic steps used to solve a problem

deductive reasoning

a system of reasoning that uses facts, definitions, or properties to reach logical conclusions

disjunction

a compound statement formed by joining 2 or more statements with the word "or

formal proof

a formal proof that contains statements and reasons organized in 2 columns

hypothesis

in a conditional statement, the statement that immediately follows the word "if

if-then statement

a compound statement of the form "If A, then B," where A and B are statements

inductive reasoning

reasoning that uses a # of specific examples to arrive at a plausible generalization or prediction. Conclusions arrived at by inductive reasoning lack the logical certainty of those arrived at by deductive reasoning

informal proof

write a paragraph to explain why a conjecture for a given situtaion is true

inverse

the statement formed by negating both the hypothesis and conclusion by a conditional statement

law of detachment

if p->q is a true conditional statement, then q is also true

law of syllogism

if p->q and q->r are true conditionals, then p-> is also true

logically equivalent

statements that have the same truth values

negation

if a statement is represented by "p," then "not p," is the negation of the statement

paragraph proof

an informal proof written in the form of a paragraph that explains why a conjecture for a given statement is true

postulate

a statement that describes a fundamental relationship between the basic terms of geometry. Postulates are accepted as true without proofs

proof

a logical argument in which each statement you make is supported by a statement that is accepted as true

related conditionals

statements such as the converse, inverse and contrapositive that are based on a given conditional statement

statement

any sentence that is either true or false, but not both

theorem

a statement or conjecture that can be proven true by undefined terms, definitions, and postulates

truth table

a table used as a convient method for organizing the truth values of statements

truth value

the truth or falsity of a statement

two column proof

a formal proof that contains statements and reasons organized in two columns. Each step is called a statement, and the properties that justify each step are called reasons