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Chapter 2 - Reasoning and Proof Flashcards

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2889393900inductive reasoningmaking a conclusion based on patterns and observations0
2889396314conjecturea concluding statement reached using inductive reasoning1
2889400308statementa sentence that is either true or false, represented using letters such as p or q2
2889401527truth valuewhether a statement is true or false3
2889424755negationa statement that has the opposite truth value, written as ~4
2889426808compound statementtwo or more statements joined together by the words "and" or "or"5
2889474269conjunctionstatements joined by the word "and", written as p^q, true when both statements are true6
2889480512disjunctionstatements joined by the work "or", written as p v q, true when at least one of the statements is true7
2889491064conditional statementa statement that can be written in if-then form, meaning "p implies q"8
2889533817hypothesisthe phrase immediately following the word "if" in a conditional statement9
2889496247conclusionthe phrase immediately following the word "then" in a conditional statement10
2889498096inverseformed by negating the hypothesis and conclusion11
2889505743converseformed by switching the hypothesis and conclusion12
2889507425contrapositiveformed by negating AND switching the hypothesis and conclusion13
2889509991bi-conditional statementthe conjunction of a conditional and its converse, "p if and only if q", true when both the conditional and the converse is true14
2926478128venn diagrama visual way of displaying the relationships between sets of data15
2926481376"all, always, every" venn diagramAll 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 diagramSome 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 diagramThere is no relationship between p and q. Two circles, p and q, that do not touch or overlap.18
2926504156deductive reasoningthe process of reasoning logically and drawing a conclusion from given facts and statements19
2926506607Law of DetachmentGiven a conditional statement, if the hypothesis is true, then the conclusion is true. If p, then q. Given p. Therefore q.20
2926509282Law of SyllogismAllows 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
2966686736Properties of EqualityProperties that keep your equation balanced.22
2966603298Addition Property of EqualityIf 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
2966604903Subtraction Property of EqualityIf 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
2966612127Multiplication Property of EqualityIf a = b, then ac = bc. (If you multiply each side of an equation by the same number, then both sides are still equal.)25
2966618096Division Property of EqualityIf 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
2966627156Distributive PropertyIf 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
2966639258Substitution Property of EqualityIf a = b, then a may be replaced by b in any expression or equation.28
2966647966Reflexive Property of EqualityIf a is a real number, then a = a. (A value will always equal itself).29
2966651643Symmetric Property of EqualityIf a = b, then b = a.30
2966658794Transitive Property of EqualityIf a = b and b = c, then a = c. ("Cuts out the middle man," like the Law of Syllogism.)31
2974256613ProofA convincing argument that uses deductive reasoning. Logically shows why a conjecture is true.32
2966664571Two-Column ProofA 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
2966670354StatementsThe steps in a proof.34
2966676334ReasonsThe justification for each step in a proof.35
2966682368Definitions, Properties, Postulates, and TheoremsWhat can be used as reasons?36
3013470802Addition (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
3013392399Reflexive Property of CongruenceFor any line segment AB, segment AB ≅ segment AB38
3013405457Symmetric Property of CongruenceIf segment AB ≅ segment CD, then segment CD ≅ segment AB.39
3013413470Transitive Property of CongruenceIf segment AB ≅ segment CD, and segment CD ≅ segment ED, then segment AB ≅ segment EF. "Cuts out the middle man"40
3013492948Reflective (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
3013420678Definition of CongruenceSegments 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
3013428736Definition of MidpointThe midpoint of a segment divides the segment into 2 equal parts. If M is the midpoint of AB, then AM = MB.43
3013500854Congruence (Definition of) Midpoint (Definition of)What are the 2 definitions that may be used in segment proofs?44
3013459240Definition of Angle BisectorAn angle bisector divides an angle into two equal parts.45
3013462787Definition of Complementary AnglesAngles are complementary if and only if the sum of their measures is 90 degrees.46
3013466530Definition of Supplementary AnglesAngles are supplementary if and only of the sum of their measures is 180 degrees.47
3013507725Definition of PerpendicularPerpendicular lines form right angles.48
3013509984Definition of a Right AngleA right angle = 90 degrees.49
3013518095Congruence (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
3013433841Segment Addition PostulateIf A, B, and C are collinear points and B is between A and C, then AB + BC = AC. "Part + Part = Whole"51
3013520826Angle Addition PostulateIf B is in the interior of 52
3013534323Vertical Angles TheoremIf two angles are vertical, then they are congruent.53
3013537130Complement TheoremIf two angles form a right angle, then they are complementary. (Right Angle --> Complementary)54
3013541205Supplement TheoremIf two angles form a liner pair, then they are supplementary. (Linear Pair --> Supplementary)55
3013545011Congruent Complements TheoremIf 56
3013553665Congruent Supplements TheoremIf 57
3013560957Vertical Angles (Theorem) Complement (Theorem) Supplement (Theorem) Congruent Complements (Theorem) Congruent Supplements (Theorem)What are the 5 theorems you may use in angle proofs?58

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