3 Conjecture: “Educated Guess” Lesson 2-1Conjecture: “Educated Guess”Inductive Reasoning: “Looking at several specific situation to arrive at a conjecture”Counterexample: “a false example of a conjecture”Vocabulary:ConjectureInductive ReasoningCounterexample
6 Lesson 2-2 Conditional: Converse: Inverse: Contrapositive: If you drive a fast car, then you drive a red car.Converse:If you drive a red car, then you drive a fast car.Inverse:If you don’t drive a fast car, then you don’t drive a red car.Contrapositive:If you don’t drive a red car, then you don’t drive a fast car.
7 Lesson 2-2 Postulate 2-1: Postulate 2-2: Postulate 2-3: Postulate 2-4: Through any two points, there is exactly one line.Postulate 2-2:Through any three points not on the same line there is exactly one plane.Postulate 2-3:A line contains at least two points.Postulate 2-4:A plane contains at least three points not on the same line.Postulate 2-5:If two points lie in a plane, then the entire line containing those points lies in that plane.Postulate 2-6:If two planes intersect, then their intersection is a line.
9 Law of Detachment Law of Syllogism No Conclusion: Lesson 2-3Law of DetachmentIf P Q and “P” exists, then “Q” existsLaw of SyllogismIf P Q and Q R, then P RNo Conclusion:If neither Law of Detachment nor Law of syllogism can be utilized then no conclusion can be metVocabulary:Looking for a patternLaw of DetachmentDeductive ReasoningLaw of Syllogism
10 Lesson 2-3 Law of Detachment Law of Syllogism If you have a car, then you can driveJason has a carConclusion: Jason can driveLaw of SyllogismIf you have drive too much, then you will run out of gasIf you run out of gas, then you will have to ask your parents for moneyConclusion: If you drive too much, then you will have to ask your parents for money
12 Reflexive property of equality Symmetric property of equality Lesson 2-4Reflexive property of equalitya = aSymmetric property of equalityIf a = b, then b = aAddition and Subtraction property of equalityIf a = b, then a + c = b + cIf a = b, then a – c = b - cMultiplication and Division property of equalityIf a = b, then a * c = b * cIf a = b, then a / c = b / cSubstitution property of equalitya = b, then a may be replaced by b in any equation or expressionDistributive property of equalitya(b + c) = ab + acVocabulary:Reflexive property of equalitySymmetric property of equalityAddition and Subtraction property of equalityMultiplication and Division property of equalitySubstitution property of equalityDistributive property of equality
13 Lesson 2-4 Two Column Proof Statement (What) a) b) c) d) e) f) ProofReason (Why) a) GIVEN b) c) d) e) f)
17 Lesson 2-42-2If two angles form a linear pair, then they are supplementary angles2-3Congruence of angles is reflexive, symmetric, and transitive2-4Angles supplementary to the same angle or to congruent angles are congruent2-5Angles complementary to the same angle or to congruent angles are congruent2-6All right angles are congruent2-7Vertical angles are congruent2-8Perpendicular lines intersect to form four right anglesVocabulary:Theorems:2-22-32-42-52-62-72-8