Geometry: Chapter 3 Terms
Order by
47 terms
Terms | Definitions |
|---|---|
 Axiom | A statement that describes a fundamental relationship between the basic terms of geometry |
| Biconditional | The conjunction of a conditional statement and it's converse |
| Compound statement | A statement formed by joining two or more statements |
| Conclusion | In a conditional statement, the statement that immediately follows the word then |
| Conditional statement | A statement that can be written in if-then form |
| Conjecture | An educated guess based on known information |
| Conjunction | A compound statement formed by joining two or more statements with the word and. |
| Contrapositive | The statement formed by negating both the hypothesis and conclusion of the converse of a conditional statement. |
| Converse | The statement formed by exchanging the hypothesis and conclusion of a conditional statement. |
| Counterexample | An example used to show that a given statement is not always true. |
| Deductive argument | A proof formed by a group of algebraic steps used to solve a problem. |
| Deductive reasoning | A system of reasoning that uses facts, rules, definitions, or properties to reach logical conclusions. |
| Disjunction | A compound statement formed by joining two or more statements with the word or. |
| formal proof | a two column proof that contains statements and reasons organized in two columns |
| hypothesis | in a conditional statement, the statement that immediately follows the word if |
| if then statement | a compound statement of the form "if a, then b" where a and b are statements |
| inductive reasoning | reasoning that uses a number of specific examples to arrive at a plausible generalization or prediction |
| informal proof | a paragraph proof |
| inverse | the statement formed by negating both the hypothesis and conclusion of a conditional statement |
| law of detachment | if p to q is a true conditional and p is true, then q is also true |
| law of syllogism | if p to q and q to r are true conditionals, then p to r is also true |
| logically equivalent | statements that have the same truth values |
| negation | if a statement is represented by p, then not p is the _________ of the statement |
| paragraph proof | an informal proof written in the form of a paragraph that explains why a conjecture for a given situation is true. |
| postulate | a statement that describes a fundamental relationship between the basic terms of geometry |
| proof | a logical argument in which each statement you make is supported by a statement that is accepted as true |
| related conditionals | statements such as the converse, inverse, and contrapositive that are based on a given conditional statement |
| statement | any sentence that is either true or false, but not both |
| theorem | a statement or conjecture that can be proven true by undefined terms, definitions, and postulates |
| truth table | a table used as a convenient method for organizing the truth values of statements. |
| truth value | the truth or falsity of a statement |
| two column proof | a formal proof that contains statements and reasons organized in two columns |
| midpoint theorem | if m is the midpoint of ab, then am is congruent to mb. |
| reflexive property | for every number a, a=a |
| symmetric property | for all numbers a and b, if a=b, then b=a |
| transitive property | for all numbers a, b, and c, if a=b+b=e, then a=c |
| addition and subtraction properties | for all numbers a, b, and c, if a=b, then a+c=b+c and a-c=b-c |
| multiplication and division properties | for all numbers a, b, and c, if a=b, then ac=bc and if c is not equal to 0, a over c =b over c |
| substitution property | for all numbers a and b, if a =b, then a may be replaced by b in any equation/expression |
| distributive property | for all numbers a,b, and c, a(b+c)=ab+ac |
| ruler postulate | the points on any line or line segment can be paired with real numbers so that, given any two points a and b on a line, a corresponds to zero and b corresponds to a positive real number |
| segment addition postulate | if b is between a and c, then ab+bc=ac |
| protractor postulate | given line ab and a number r between 0 and 180, there is exactly one ray with endpoint a extending on either side of line ab, such that the measure of the angle formed is r. |
| angle addition postulate | if r is in the interior of angle pqs, then pqr+rqs=pqs. if pqr_rqs=pqs, then r is in the interior of pqs |
| supplementary theorem | if two angles form a linear pair then they are supplementary angles |
| complement theorem | if the noncommon sides of two adjacent angles form a right angle, then the angles are complementary angles |
| vertical angles theorem | if two angles are vertical angles, then they are congruent |
First Time Here?
Welcome to Quizlet, a fun, free place to study. Try these flashcards, find others to study, or make your own.