GEOMETRY UNIT 2

truth value

the degree of truth of a conditional statement.

negation

the negative for of any part of a conditional statement

reasoning

the of act of forming conclusions based on available information.

biconditional statement

a logical statement formed by the combination of a conditional statement and its converse.

expression

a number, symbol, or group of numbers and/or symbols with their operations used to express some mathematical fact, quantity, or value.

algebraic proof

a proof that uses algebraic properties to reach a conclusion about an algebraic equation.

geometric property

a property that compares the congruence of one geometric figure with the same or another geometric figure.

converse of a conditional statement

a related conditional statement in which the hypothesis and the conclusion of a conditional statement have been exchanged.

contrastive of a conditional statement

a related conditional statement resulting from the exchange and negation of both the hypothesis and conclusion of a conditional statement.

inverse of a conditional statement

a related conditional statement resulting from the negation of the hypothesis and conclusion of a conditional statement.

argument

a series of reasons that leads to a conclusion.

conjecture

a statement concluded to be true based on logical reasoning.

conditional statement

a statement in which a conclusion is true if the conditions of a particular hypothesis are true.

theorem

a statement or conjecture that can be proven by undefined terms, definitions, postulates, and previously proven theorems.

algebraic property

a universally exceoted statement about an algebraic expression or equation that holds trie in every instance in which the conditions of the property are met.

definition

a biconditional statement that is used to describe a geometric object or concept.

counterexample

an example that proves a conjecture false.

related conditional statement

the converse, inverse, and contrapositive of a conditional statement.

conclusion

the part of a conditional statement that expresses the action that will result if the conditions of the statement are met.

hypothesis

the part of a conditional statement that expresses the conditions that must be met by the statement.

inductive reasoning

the process of reasoning that a rule, condition, definition, property, or statement is true because specific cases have been observed to be true.

justification

the statement of the reason for each step in a proof.

valid argument

an application of deductivereasoning such that the reasoning is logically correct and undeniably true.

proof

an argument that uses logic in the form of definitions, properties, and previously proved principles to show that a conclusion is true.

formal proof

an argument that uses logic without written justification in the form of definitions, properties, and previously proved geometric principles to show that a conclusion is true.

informal proof

an argument that uses logic without written justification to show that a conclusion is true.

geometric proof

an argument that uses written justification in the form of definitions, properties, postulates, and previously proved theorems and corollaries to show that a conclusion is true.

congruent angles

angles that have the same measure

Linear Pair Theorem

if any two angles form a linear pair, then they are supplementary.

conjunction

a compound logic statement made up of two statements joined together with that word "and" ; p^q.

Law of Detachment

a law of deductive reasoning that states that if a conditional statement is true and its hypothesis is true, then its conclusion will also be true[(p>q)^p]>q.

Law of Syllogism

a law of deductive reasoning that states that if two conditional statements are true, and if the conclusion of the first statement is the hypothesis of the second statement, then a conclusion based on the conditional statements will also be true; [(p>q)^(q>r)]>(p>r).