2889393900 | inductive reasoning | making a conclusion based on patterns and observations | | 0 |
2889396314 | conjecture | a concluding statement reached using inductive reasoning | | 1 |
2889400308 | statement | a sentence that is either true or false, represented using letters such as p or q | | 2 |
2889401527 | truth value | whether a statement is true or false | | 3 |
2889424755 | negation | a statement that has the opposite truth value, written as ~ | | 4 |
2889426808 | compound statement | two or more statements joined together by the words "and" or "or" | | 5 |
2889474269 | conjunction | statements joined by the word "and", written as p^q, true when both statements are true | | 6 |
2889480512 | disjunction | statements joined by the work "or", written as p v q, true when at least one of the statements is true | | 7 |
2889491064 | conditional statement | a statement that can be written in if-then form, meaning "p implies q" | | 8 |
2889533817 | hypothesis | the phrase immediately following the word "if" in a conditional statement | | 9 |
2889496247 | conclusion | the phrase immediately following the word "then" in a conditional statement | | 10 |
2889498096 | inverse | formed by negating the hypothesis and conclusion | | 11 |
2889505743 | converse | formed by switching the hypothesis and conclusion | | 12 |
2889507425 | contrapositive | formed by negating AND switching the hypothesis and conclusion | | 13 |
2889509991 | bi-conditional statement | the conjunction of a conditional and its converse, "p if and only if q", true when both the conditional and the converse is true | | 14 |
2926478128 | venn diagram | a visual way of displaying the relationships between sets of data | | 15 |
2926481376 | "all, always, every" venn diagram | All elements of p are elements of q.
Little circle p completely inside of big circle q.
If p, then q. | | 16 |
2926482821 | "some, sometimes" venn diagram | Some elements of p are elements of q.
Two circles, p and q, that have an overlap.
p and q (overlap part)
p or q (everything in both circles) | | 17 |
2926486330 | "never, no, none" venn diagram | There is no relationship between p and q.
Two circles, p and q, that do not touch or overlap. | | 18 |
2926504156 | deductive reasoning | the process of reasoning logically and drawing a conclusion from given facts and statements | | 19 |
2926506607 | Law of Detachment | Given a conditional statement, if the hypothesis is true, then the conclusion is true.
If p, then q.
Given p.
Therefore q. | | 20 |
2926509282 | 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.
If p, then q.
If q, then r.
Therefore, If p, then r. | | 21 |
2966686736 | Properties of Equality | Properties that keep your equation balanced. | | 22 |
2966603298 | Addition Property of Equality | If a = b, then a + c = b + c.
(If you add the same number to each side of an equation, then both sides are still equal.) | | 23 |
2966604903 | Subtraction Property of Equality | If a = b, then a - c = b - c.
(If you subtract the same number from each side of an equation, then both sides are still equal.) | | 24 |
2966612127 | Multiplication Property of Equality | If a = b, then ac = bc.
(If you multiply each side of an equation by the same number, then both sides are still equal.) | | 25 |
2966618096 | Division Property of Equality | If a = b, then a/c = b/c.
(If you divide each side of an equation by the same number, then both sides are still equal.) | | 26 |
2966627156 | Distributive Property | If a(b+c), then a(b+c) = ab + ac.
(If you multiply a sum by a number, then you will get the same result if you multiply each addend by that number and then add the products.) | | 27 |
2966639258 | Substitution Property of Equality | If a = b, then a may be replaced by b in any expression or equation. | | 28 |
2966647966 | Reflexive Property of Equality | If a is a real number, then a = a.
(A value will always equal itself). | | 29 |
2966651643 | Symmetric Property of Equality | If a = b, then b = a. | | 30 |
2966658794 | Transitive Property of Equality | If a = b and b = c, then a = c.
("Cuts out the middle man," like the Law of Syllogism.) | | 31 |
2974256613 | Proof | A convincing argument that uses deductive reasoning. Logically shows why a conjecture is true. | | 32 |
2966664571 | Two-Column Proof | A common format used to organize a proof where statements are on the left and their corresponding reason is on the right. Each statement must follow logically from the steps before it. | | 33 |
2966670354 | Statements | The steps in a proof. | | 34 |
2966676334 | Reasons | The justification for each step in a proof. | | 35 |
2966682368 | Definitions, Properties, Postulates, and Theorems | What can be used as reasons? | | 36 |
3013470802 | Addition (Property of Equality)
Subtraction (Property of Equality)
Multiplication (Property of Equality)
Division (Property of Equality)
Distributive (Property)
Substitution (Property)
Reflective (Property of Equality)
Symmetric (Property of Equality)
Transitive (Property of Equality) | What are the 9 properties that may used only with equal signs? | | 37 |
3013392399 | Reflexive Property of Congruence | For any line segment AB, segment AB ≅ segment AB | | 38 |
3013405457 | Symmetric Property of Congruence | If segment AB ≅ segment CD, then segment CD ≅ segment AB. | | 39 |
3013413470 | Transitive Property of Congruence | If segment AB ≅ segment CD, and segment CD ≅ segment ED, then segment AB ≅ segment EF.
"Cuts out the middle man" | | 40 |
3013492948 | Reflective (Property of Congruence)
Symmetric (Property of Congruence)
Transitive (Property of Congruence) | What are the 3 properties that may be applied to statements with congruence symbols? | | 41 |
3013420678 | Definition of Congruence | Segments are congruent if and only if they have the same measure:
If segment AB ≅ segment CD, then AB = CD.
If AB = CD, then segment AB ≅ segment CD. | | 42 |
3013428736 | Definition of Midpoint | The midpoint of a segment divides the segment into 2 equal parts.
If M is the midpoint of AB, then AM = MB. | | 43 |
3013500854 | Congruence (Definition of)
Midpoint (Definition of) | What are the 2 definitions that may be used in segment proofs? | | 44 |
3013459240 | Definition of Angle Bisector | An angle bisector divides an angle into two equal parts. | | 45 |
3013462787 | Definition of Complementary Angles | Angles are complementary if and only if the sum of their measures is 90 degrees. | | 46 |
3013466530 | Definition of Supplementary Angles | Angles are supplementary if and only of the sum of their measures is 180 degrees. | | 47 |
3013507725 | Definition of Perpendicular | Perpendicular lines form right angles. | | 48 |
3013509984 | Definition of a Right Angle | A right angle = 90 degrees. | | 49 |
3013518095 | Congruence (Definition of)
Angle Bisector (Definition of)
Complementary Angles (Definition of)
Supplementary Angles (Definition of)
Perpendicular (Definition of)
Right Angle (Definition of a) | What are the 6 definitions that may be used in angle proofs? | | 50 |
3013433841 | Segment Addition Postulate | If A, B, and C are collinear points and B is between A and C, then AB + BC = AC.
"Part + Part = Whole" | | 51 |
3013520826 | Angle Addition Postulate | If B is in the interior of | | 52 |
3013534323 | Vertical Angles Theorem | If two angles are vertical, then they are congruent. | | 53 |
3013537130 | Complement Theorem | If two angles form a right angle, then they are complementary. (Right Angle --> Complementary) | | 54 |
3013541205 | Supplement Theorem | If two angles form a liner pair, then they are supplementary. (Linear Pair --> Supplementary) | | 55 |
3013545011 | Congruent Complements Theorem | If | | 56 |
3013553665 | Congruent Supplements Theorem | If | | 57 |
3013560957 | Vertical Angles (Theorem)
Complement (Theorem)
Supplement (Theorem)
Congruent Complements (Theorem)
Congruent Supplements (Theorem) | What are the 5 theorems you may use in angle proofs? | | 58 |