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32 terms

geometry vocab chapter 2

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axiom
a statement that describes a fundamental relationship between the basic terms of geometry
biconditional
the conjunction of a conditional statement and its converse
compound statement
a statement formed by joining two ore more statements
conclusion
the phrase that immediately follows the word then
conditional statement
a statement that can be written in if-then form
conjecture
an educated guess based on known information
conjunction
a compound statement formed by joining two ore more statements within the word and.
contrapositive
the statement formed by negating both the hypothesis and conclusion of the converse of a conditional statement
converse
the statement formed by exchanging the hypothesis and conclusion of a conditional statement
counterexample
an example used to show that the 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, rules, definitions, or properties to reach logical conclusions
disjunction
a compound statement formed by joining two or more statements with the word or
formal proof
statements and reasons organized in two columns
hypothesis
the phrase immediately following the word if
if-then statement
written in the form if p, then q.
inductive reasoning
uses a number of specific examples to arrive at a plausible generalization
informal proof
you write a paragraph to explain why a conjecture for a given situation is true
inverse
negating both the hypothesis and conclusion of the conditional
Law of Detachment
a form of deductive reasoning that is used to draw conclusions from true conditional statements
Law of Syllogism
similar to the transitive property of equality
logically equivalent
statements with the same truth values
negation
has the opposite meaning as well as an opposite truth value
paragraph proof
write a paragraph to explain why a conjecture for a given situation is true
postulate
statement that describes a fundamental relationship between the basic terms of geometry
proof
a logical argument in which each statement you make is supported by a statement that is accepted as true
related conditionals
other statements 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 convenient method for organizing the truth values of statements
truth value
the truth of falsity of a statement
two-column proof
containing statements and reasons organized in two columns.