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