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Chapter 2 Vocab
Geometry - Mrs. Sprouse
| Term | Definition |
|---|---|
| inductive reasoning | making a conclusion based on observations and patterns |
| conjecture | a concluding statement reached using inductive reasoning |
| counterexample | an example that shows a conjecture is false |
| statement | a sentence that is either true or false |
| statement | called the truth value |
| statement | represented by using letters such as p or q |
| negation | opposite truth value |
| negation | shown by the symbol ~ |
| compound statements | two or more statements joined by the words "and" or "or" |
| conjunction | statements joined by the word "and" |
| conjunction | written as p ^ q |
| conjunction | true when both statements are true |
| disjunction | statements joined by the word "or" |
| disjunction | true when at least one statement is true |
| truth tables | a convenient way or organizing truth values of statements |
| conditional statements | a statement that can be written in "if, then" form |
| p -> q | symbolic form for conditional statements |
| inverse statements | formed by negating the hypothesis and conclusion |
| ~p -> ~q | symbolic form for inverse statements |
| q -> p | symbolic form for converse statements |
| converse statements | formed by switching the hypothesis and conclusion |
| contrapositive statements | formed by negating and switching the hypothesis and conclusion |
| ~q -> ~p | symbolic form for contrapositive statements |
| biconditional statements | the conjunction of the conditional and its converse |
| p <--> q | symbolic form for biconditional statements |
| biconditional statements | read as "p if and only q" |
| biconditional statements | true when both conditional and converse are true |
| deductive reasoning | the process of reasoning logically and drawing a conclusion from given facts and statements |
| Law of Detachment | given a conditional statement "If the hypothesis is true, then the conclusion is true." |
| Law of Syllogism | allows you to draw a conclusion from two conditional statements in which the conclusion of the first statement is the hypothesis of the second statement |
| 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 |
| Substitution Property of Equality | If a=b, then a may be replaced by b in any expression or equation. |
| Distributive Property | a(b+c), then a(b+c) = ac + bc |
| Reflexive Property of Equality | a value always will equal itself |
| Symmetric Property of Equality | If a=b, then b=a |
| Transitive Property of Equality | If a=b and b=c, then a=c |
| two-column proof | a common format used to organize a proof |
| Reflexive Property of Congruence | For any segment AB, segment AB is congruent to segment AB. |
| Symmetric Property of Congruence | If segment AB is congruent to segment CD, then segment CD is congruent to segment AB. |
| Transitive Property of Congruence | If segment AB is congruent to segment CD and segment CD is congruent to segment EF, then segment AB is congruent to segment EF. |
| Definition of Congruence | Segments are congruent if and only if they have the same measure. |
| Definition of Congruence | If segment AB is congruent to segment CD, then AB = CD. If AB = CD, then segment AB is congruent to segment CD. |
| Definition of Midpoint | The midpoint of a segment divides the segment into two congruent parts (equal lengths). |
| Definition of a Right Angle | An angle measures 90 degrees if and only it is a right angle. |
| Definition of Complementary Angles | Two angles are complementary if and only if the sum of their measures is 90 degrees. |
| Definition of Supplementary Angles | Tow angles are supplementary if and only the sum of their measures is 180 degrees. |
| Definition of an Angle Bisector | An angle bisector divides an angle into two equal parts. |
| Definition of Perpendicular | Perpendicular lines form right angles. |
| Vertical Angles Theorem | If two angles are vertical, then they are congruent. |
| Complement Theorem | If two angles form a right angle, then they are complementary. |
| Linear Pair Theorem | If two angles form a linear pair, then they are supplementary. (lp) |
| Supplement Theorem | If two angles form a linear pair, then they are supplementary. (s) |
| Congruent Complements Theorem | If two angles are complementary to the same angle, then they are congruent. |
| Congruent Supplements Theorem | If two angles are supplementary to the same angle, then they are congruent. |
| Congruent Complements Theorem | If <A is complementary to <B, and <C is complementary to <B, then <A is congruent to <C. |
| Congruent Supplements Theorem | If <A is supplementary to <B, and C is supplementary to <B, then <A is congruent to <C. |
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