251520
| Question | Answer |
| Conjecture | A statement you believe to be true based on inductive reasoning. |
| Counterexample | A drawing, statement, or a picture for when the conjecture is false. |
| Conditional Statement | A statement that can be written in the form "if p, then q" p --> q |
| Hypothesis | The part P of the conditional statement following the word if. |
| Conclusion | The part q in the conditional statement following the word then. |
| Truth Value | True or False (A conditional statement is only false when the hypothesis is true and the conclusion is false. |
| Negation | Of the statement p is "not p" written as ~p |
| Converse | The statement formed by exchanging the hypothesis and conclusion. q --> p |
| Inverse | The statement formed by negating the hypothesis and conclusion. ~p --> ~q |
| Contrapositive | The statement formed by both exchanging and negating the hypothesis and conclusion. ~q --> ~p |
| Logically Equivalent Statements | Related conditional statements that have the same truth value. |
| Biconditional Statement | A statement that can be written in the form "p if and only if q" This means "if p, then q" and "if q, then p" |
| Definition | A statement that describes a mathematical object and can be written as a true biconditional. |
| Polygon | A closed plane figure formed by three or more line segments. |
| Triangle | A three-sided polygon. |
| Quadrilateral | A four-sided polygon. |
| Proof | An argument that uses logic, definitions and properties and previously proven statements 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, the ac = bc |
| Division Property of Equality | If a = b , then a/c = b/c |
| Reflexive Property of Equality/Congruence | a=a |
| Symmetric Property of Equality/Congruence | If a = b, then b = a |
| Transitive Property of Equality/Congruence | 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. |
| Theorem | Any statement that you can prove. (Once you have proven a statement you can use it as a reason in later proofs) |
| Two-Column Proof | You list the steps of the proof in the left column, you list the matching reason for each step in the right column. |
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