Unit 2: Reasoning and Proof Test Review
Two-column proof
a format for a proof that has numbered statements and corresponding reasons that show an argument in a logical order
Paragraph proof
a format for a proof that presents the statements and reasons of a proof as sentences in a paragraph
Flowchart proof
a format for a proof that uses boxes and arrows to show the flow of a logical argument
Line Perpendicular to a Plane
a line intersects a plane on a point and is perpendicular to every line in the plane that intersects at that point
Proof
a logical argument that uses deductive reasoning to show that a statement is true.
Conditional Statement
a logical statement that has two parts, a hypothesis and a conclusion. If p, then q.
Inductive Reasoning
a process that involves looking for patterns and making conjectures
Deductive Reasoning
a process that uses facts, definitions, accepted properties and the laws of logic to form logical arguments
Counterexample
a specific case for which the conjecture is false
Theorem
a statement in geometry that must be proven true
Converse
a statement that exchanges the hypothesis and the conclusion of a conditional statement. If q, then p.
Contrapositive
a statement that negates both hypothesis and the conclusion of the CONVERSE of a conditional statement
Inverse
a statement that negates both the hypothesis and the conclusion of a conditional statement. If not p, then not q.
Conjecture
an unproven statement that is based on observations
Hypothesis
p, follows the if
Conclusion
q, follows the then
Negation
the opposite of the original statement
Perpendicular Lines
two lines that intersect to form a right angle
Biconditional Statement
written when a conditional statement and its converse are BOTH true. p if and only if q.