GEOMETRY FUNDAMENTALS - UNIT 11 Essays (384 words) - Logic

GEOMETRY FUNDAMENTALS - UNIT 11 REVIEW GEOMETRY PROOFS ConclusionThe then clause in a conditional statement.ConditionalA statement formed from two statements by connecting them in the form if ______ , then ______ .ConjunctionA statement formed by combining two statements with the word and.ContrapositiveA statement formed by exchanging the hypothesis and conclusion and negating both of them.ConverseA statement formed by interchanging the hypothesis and the conclusion in a conditional statement.Deductive reasoningThe process of making a conclusion about a specific statement by supporting with general rules and principles.DisjunctionA statement formed by combining two statements with the word or.HypothesisThe if clause in a conditional statement.Indirect proofA proof of a theorem by indirect means.Inductive reasoningThe process of drawing a general conclusion based on specific examples.InverseA statement formed by negating both the hypothesis and the conclusion of a conditional statement.NegationIf p is a statement, the new statement, not p is called the negation of p.true-false statementA sentence that is either true or false but not both.Truth tableAn arrangement of truth values to determine when a statement is true or false.Two-column ProofA formal proof of a theorem composed of six standard parts. The normal method of an indirect proof is to follow the three steps outlined here.1 Assume the theorem you are proving is false.2 Reason from your assumed statement until you reach a contradiction of a known fact, theorem, or axiom. 3 Point out why the assumed statement must be incorrect and therefore the theorem must be true. The six parts of a two-column proof are listed in order: Statement: a full written statement of the theorem. Figure: a lettered figure drawn to illustrate the given conditions of the statement. Given: the given conditions of the statement expressed in terms of the letter and numerals used in the figure. To prove: the part of the statement that requires proof expressed in terms of the letters and numerals that are used in the figure. Plan of proof: a brief description of the plan you are going to use in the proof. Proof: the actual proof; a series of numbered statements in one column with a like-numbered column next to it for the reasons.