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Chapter 2 Review Lessons 2-1 through 2-6. LESSON 2-1 Inductive Reasoning and Conjecturing.

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Presentation on theme: "Chapter 2 Review Lessons 2-1 through 2-6. LESSON 2-1 Inductive Reasoning and Conjecturing."— Presentation transcript:

1 Chapter 2 Review Lessons 2-1 through 2-6

2 LESSON 2-1 Inductive Reasoning and Conjecturing

3 Lesson 2-1 Conjecture: Educated Guess Inductive Reasoning: Looking at several specific situation to arrive at a conjecture Counterexample: a false example of a conjecture Vocabulary: Conjecture Inductive Reasoning Counterexample

4 LESSON 2-2 If-Then Statements and Postulates

5 Lesson 2-2 If-then statements: – Conditional statement P Q Hypothesis P Conclusion Q – Converse: – Q P Negation: (~) – Not – Inverse: – ~P ~Q – Contrapositive: ~Q ~P Vocabulary: If-then statements Conditional statements Hypothesis P Conclusion Q Converse Negation Inverse Contrapositive Venn Diagram

6 Lesson 2-2 Conditional: – 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 dont drive a fast car, then you dont drive a red car. Contrapositive: – If you dont drive a red car, then you dont drive a fast car.

7 Lesson 2-2 Postulate 2-1: – 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.

8 LESSON 2-3 Deductive Reasoning

9 Lesson 2-3 Law of Detachment – If P Q and P exists, then Q exists Law of Syllogism – If P Q and Q R, then P R No Conclusion: – If neither Law of Detachment nor Law of syllogism can be utilized then no conclusion can be met Vocabulary: Looking for a pattern Law of Detachment Deductive Reasoning Law of Syllogism

10 Lesson 2-3 Law of Detachment (1)If you have a car, then you can drive (2)Jason has a car Conclusion: Jason can drive Law of Syllogism (1)If you have drive too much, then you will run out of gas (2)If you run out of gas, then you will have to ask your parents for money Conclusion: If you drive too much, then you will have to ask your parents for money

11 LESSON 2-4 Using Proof in Algebra

12 Lesson 2-4 Reflexive property of equality a = a Symmetric property of equality If a = b, then b = a Addition and Subtraction property of equality If a = b, then a + c = b + c If a = b, then a – c = b - c Multiplication and Division property of equality If a = b, then a * c = b * c If a = b, then a / c = b / c Substitution property of equality a = b, then a may be replaced by b in any equation or expression Distributive property of equality a(b + c) = ab + ac Vocabulary: Reflexive property of equality Symmetric property of equality Addition and Subtraction property of equality Multiplication and Division property of equality Substitution property of equality Distributive property of equality

13 Lesson 2-4 Two Column Proof Statement (What) a) b) c) d) e) f) Proof Reason (Why) a) GIVEN b) c) d) e) f)

14 LESSON 2-5 Verifying Segment Relationships

15 Lesson 2-5 Theorem Congruence of segments is: Reflexive Symmetric Transitive Vocabulary: Theorem 2-1

16 LESSON 2-6 Verifying Angle Relationships

17 Lesson – If two angles form a linear pair, then they are supplementary angles 2-3 – Congruence of angles is reflexive, symmetric, and transitive 2-4 – Angles supplementary to the same angle or to congruent angles are congruent 2-5 – Angles complementary to the same angle or to congruent angles are congruent 2-6 – All right angles are congruent 2-7 – Vertical angles are congruent 2-8 – Perpendicular lines intersect to form four right angles Vocabulary: Theorems:


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