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# Geometry Ch. 2

### Geometric Reasoning- vocabulary

TermDefinition
inductive reasoning the process of reasoning that a rule or statement is true because specific cases are true
conjecture a statement believed to be true based on inductive reasoning
counterexample an example that proves a conjecture or statement is false
conditional statement (words) "if p, then q"
hypothesis the part p of a conditional statement following the word 'if'
conclusion the part q of a conditional statement following the word 'then'
conditional statement (symbols) p --> q
negation of p (symbols) ~p
negation of p (words) "not p"
converse (words) the statement formed by exchanging the hypothesis and conclusion
converse (symbols) q --> p
inverse (words) the statement formed by negating the hypothesis and the conclusion
inverse (symbols) ~p --> ~q
contrapositive (words) the statement formed by exchanging AND negating the hypothesis and conclusion
contrapositive (symbols) ~q --> ~p
logically equivalent statements statements that have the same truth value
deductive reasoning the process of using logic to draw conclussions
Law of Detachment if p-->q is true and p is true, then q is true
Law of Syllogism if p-->q and q-->r are true statements, then p-->r is a true statement
biconditional statement a statement that can be in the form "p if and only if q"
definition a statement that describes a mathematical object and can be written as a true biconditional statement.
polygon a closed plane figure formed by three or more segments such that each segment intersects exactly two other segments only at their endpoints and no two segments with a common endpoint are collinear
triangle a three sided polygon
proof an argument that uses logic to show that a conclusion is true
Addition Property of Equality If a = b, then a + c = b + c.
Subtraction Property of Equality If a = b, then a - c = b - c.
Multiplication Property of Equality If a = b, then ac = bc.
Division Property of Equality If a = b, then a/c = b/c.
Reflexive Property of Equality a = a
Symmetric Property of Equality If a = b, then b = a.
Transitive Property of Equality If a = b and b = c, then a = c.
Substitution Property of Equality If a = b, then b can be substituted for a in any expression.
Distributive Property a(b + c) = ab + ac
Reflexive Property of Congruence figure A ≅ figure A
Symmetric Property of Congruence If figure A ≅ figure B, then figure B ≅ figure A.
Transitive Property of Congruence If figure A ≅ figure B and figure B ≅ figure C, then figure A ≅ figure C.
theorem a statement that has been proven
two-column proof a style of proof in which the statements are written in the left-hand column and the reasons are written in the right-hand column
flowchart proof a style of proof that uses boxes and arrows to show the structure of the proof
paragraph proof a style of proof in which the statements and reasons are presented in paragraph form
Created by: rivey