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31 terms

H Geometry unit 2

vocabulary for unit 2
STUDY
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argument
a fact or assertion offered as evidence that something is true
conclusion
the proposition arrived at by logical reasoning (such as the proposition that must follow from the major and minor premises of a syllogism)
deductive reasoning
reasoning in which a conclusion is reached by stating a general principle and then applying that principle to a specific case (The sun rises every morning; therefore, the sun will rise on Tuesday morning.)
diagonals
a segment that connects two vertices that are not next to each other
premise
a statement that is assumed to be true and from which a conclusion can be drawn
proof
a formal series of statements showing that if one thing is true something else necessarily follows from it
syllogism
deductive reasoning in which a conclusion is derived from two premises
valid argument
an argument in which the reasons support the conclusion so that the conclusion follows from the reasons offered.
conditional statement
a type of logical statement that has two parts, a hypothesis and a conclusion
contrapositive
the statement formed when you negate the hypothesis and conclusion of the converse of a conditional statement
converse
the statement formed by switching the hypothesis and conclusion of a conditional statement
hypothesis
a proposal intended to explain certain facts or observations
inverse
the statement formed when you negate the hypothesis and conclusion of a conditional statement
logical chain
A series of rationally linked conditional statements
statement
a fact or assertion offered as evidence that something is true
truth-functionally equivalent
for every combination of truth values that we make, these expressions will yield the same truth value
compound statement
a statement formed by joining two or more statements
conjunction
a compound statement formed by joining two or more statements with the word and
contradiction
a statement that is the opposite of another statement
disjunction
a compound statement formed by joining two or more statements with the word or
exclusive or
one and only one of the simple sentence is true
inclusive or
one or both of the simple sentence are true(the one word that we use)
indirect proof
a type of proof where it is first assumed that the statement is false. If the assumption leads to an impossibility, than the original statement has to be proven true
proof by contradiction
a form of proof that establishes the truth or validity of a proposition by showing that the proposition being false would imply a contradiction
conjecture
reasoning that involves the formation of conclusions from incomplete evidence
direct proof
a proof that starts with the given statements and uses the laws of logic to arrive at the statement to be proved
theorem
a true statement that follows as a result of other true statements
two-column proof
a type of proof written as numbered statements and reasons that show the logical order of an argument
inductive reasoning
reasoning from detailed facts to general principles
paragraph proof
an informal proof written in the form of a paragraph that explains why a conjecture for a given situation is true
vertical angles
a pair of opposite congruent angles formed by intersecting lines