| A | B |
|---|
| Conclusion | The phrase immediately following the word then-p →q, read if p then q, or p implies q→p |
| Converse | Exchanging the hypothesis and conclusion of the conditional-q→p (If two angles are congruent, then they have the same measure.) |
| Inverse | Negatomg both the hypothesis and conclusion of the conditional-~p→~q(If two angles do not have the same measure, then they are not congruent.) |
| Contrapositive | Negating both the hypothesis and conclusion of the converse statement-~q→~p(If two angles are not congruent, then they do not have the same measure.) |
| Conditional | Given hypothesis and conclusion-p→1 (If 2 angles have the same measure, then they are congruent.) |
| If given a conditional is true, | The converse and the inverse are not necessarily true. |
| The contrapositive | Of a false conditional is always false. |
| The converse and the inverse of a conditional | Are either both true or both false. |
| Logically Equivalent | Statements with the same truth values are said to be this (A conditional and its contrapositive are logically equivalent as are the converse and inverse of a conditional.) |
| Law of Detachment | A form of deductive reasoning that is used to draw conclusions from true conditional statements |
| Law of Syllogism | A law of logic: if a --> b, b -->c, then a -->c |
| Proof | A logical argument in which each statement you make is supported by a statement that is accepted as true. |
| Theorem | Once a statement or conjecture has been shown to be true |
| Deductive Argument | A group of algebraic steps used to solve problems |
| Segment Addition Postulate | If B is between A and C, then AB+BC=AC |
| Reflexive Property | For every a, a=a. |
| Symmetric Property | For all numbers a, b, and c, if a=b, then a+c=b+c. |
| Transitive Property | For all numbers a, b, and c, if a=b and b=c, then a=c |
| Angle Addition Postulate | If R is the interior of <PQS, then m<RQS=mPQS, then R is in the interior of <PQS. |
| Supplement 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. |
| Perpendicular Lines | Intersectt to form four right angles |
| All right angles | Are congruent |
| Perpendicular Lines form | Congruent adjacent angles |
| If wo angles are congruent and supplementary | Then each angle is a right angle |
| If two congruent angles form a linear pair, | Then they are right angles |
| Conjectures are based upon | Observations and patterns |
| Counterexamples can be used | To show that a conjecture is false |
| hypothesis symbol | p |
| conclusion | q |
| conditional statement symbols | p --> q |
| inverse symbols | ~p --> ~q |
| converse symbols | q --> p |
| contrapositive symbols | ~q --> ~p |
