Geometry Logic: Conditional Statements, Conjectures, and Proofs

conditional statement

A logical statement that has a hypothesis and a conclusion. p —> q

hypothesis

The 'if' part of the statement.

conclusion

The 'then' part of the statement.

converse

The statement formed by exchanging the hypothesis and conclusion of a conditional statement. q —> p

contrapositive

The statement formed by negating both the hypothesis and conclusion of the converse of a conditional statement. ~q—>~p

biconditional statement

a statement that contains "if and only if" - p<—>q

flow chart proof (flow proof)

used boxes and arrows to show the flow of a logical argument

if-then form

the "if" part (hypothesis), "then" part (conclusion)

inverse

negate both the hypothesis and the conclusion. ~p —> ~q

line perpendicular to a plane

if and only if the line intersects the plane in a point and is perpendicular to every line in the plane that intersects it at that point

narrative proof

presents the statements and reasons of a proof as sentences in a paragraph

paragraph proof

presents the statements and reasons of a proof as sentences in a paragraph

perpendicular lines

lines that intersect to form right angles

proof

logical argument that uses deductive reasoning to show that a statement is true

counterexample

A specific case for which a conjecture is false.

deductive reasoning

A process that uses facts, definitions, accepted properties, and the laws of logic to form a logical argument.

inductive reasoning

A method of reasoning that involves making generalizations based on specific observations.

conjecture

An unproven statement that is based on observations.

theorem

A statement that has been proven based on previously established statements and axioms.

two-column proof

A method of proving statements in geometry that lists statements and reasons in two columns.

negation

The opposite of a given statement.

equivalent statement

Statements that have the same truth value in every possible scenario.