| A | B |
|---|
| 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 and b = c, 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 a . c = b . c, and if c =/= 0, a/c = b/c. |
| Substitution Property | For all numbers a and b, if a = b, then a may be replaced by b in any equation or expression. |
| Distributive Property | For all numbers a, b, and c, a(b + c) = ab + ac. |
| Reflexive (Segments & Angles) | Seg: PQ = PQ & Angles: m<1 = m<1 |
| Symmetric Property (Segments & Angles) | Seg: If AB = CD, then CD = AB. If m<A = m<B, then m<B = m<A. |
| Transitive (Segments & Angles) | Seg: If GH = JK and JK = LM, then GH = LM. Angles: If m< 1 = m<2 and m<2 = m<3, then m<l = m<3. |
| Proof | Reasons (properties) listed for each step leading to the conclusion |
| Two-Column proof | Proofs wrieetn in two columns |
| A conjecture | an educated guess |
| inductive reasoning | looking at several specific situations to arrive at a conjecture |
| counterexample | a false example - it only takes 1 false example to show that a conjecture is not true |
| conditional statements (Also called conditionals) | If-then statements |
| hypothesis | In a conditional statement the portion of the sentence following IF |
| conclusion | In a conditional statement the portion of the sentence following THEN |
| If & then are not used | when you write the hypothesis or the conclusion |
| The converse of p-->q | q-->p |
| ~p represents | not p |
| The inverse of p-->q | ~p-->~q |
| The contrapositive of p-->q | ~q-->~p |
| The converse or inverse of a true statement | is not necessarily true |
| The contrapositive of a conditional | The contrapositive of a true conditional is always true and the contrapositive of a false conditional is always false |
| Postulates | principles that are accepted to be true |
| P-through any two points | there is exactly one line |
| P-through any three points not on the same line | there is exactly one plane |
| P-a line contains | at least two points |
| P-a plane contains | at least three points not on the same line |
| P-if two points lie in a plane | then the entire line containing those two points lies in that plane |
| P-If two planes intersect | then their intersection is a line |
| Venn diagram | can be used to illustrate a conditional |
| Law of detachment | If p-->q is a true conditional and p is true, then q is true |
| Deductive reasoning | uses a rule to make a conclusion |
| Inductive reasoning | uses examples to make a conjecture or rule |
| Law of Syllogism | If p-->q and q-->r are true conditionals, then p-->r is also true (similar to transitive property of equality) |
| T-Congruence of segments | is reflexive, symmetric, and transitive |
| Supplement Theorem | If two angles form a linear pair, then they are supplementary angles |
| T-Congruence of angles | is reflexive, symmetric, and transitive |
| T-Angles supplementary | to the same angle or to congruent angles are congruent |
| T-Angles complementary | to the same angle or to congruent angles are congruent |
| T-All right angles | are congruent |
| T-Vertical angles | are congruent |
| T-Perpendicular lines | intersect to form four right angles |
| Ch-1 Postulate 1-1 Ruler Postulate | Given any two points P and Q on a line. P corresponds to zero, and Q corresponds to a positive number. |
| Ch-1 Postulate 1-2 Segment Addition Postulate | If Q is between P and R, then PQ + QR = PR; If PQ + QR = PR, then Q is between P and R. |
| Ch-1 Protractor Postulate | there can only be one 55 degree angle on either side of a given ray |
| Ch-1 Angle Addition Postulate | If R is in the interior of <PQS, then m<PQR + m<RQS = m<PQS. If m<PQR + m<RQS = m<PQS, then R is in the interior of <PQS |
