Chapter 2 Review Lessons 2-1 through 2-6

Inductive Reasoning and Conjecturing Lesson 2-1

Conjecture: “Educated Guess” 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

If-Then Statements and Postulates Lesson 2-2

If-then statements: Negation: (~) – “Not” Conditional statement 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

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.

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.

Deductive Reasoning Lesson 2-3

Law of Detachment Law of Syllogism No Conclusion: 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

Lesson 2-3 Law of Detachment Law of Syllogism If you have a car, then you can drive Jason has a car Conclusion: Jason can drive Law of Syllogism If you have drive too much, then you will run out of gas 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

Using Proof in Algebra Lesson 2-4

Reflexive property of equality Symmetric property of equality 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

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

Verifying Segment Relationships Lesson 2-5

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

Verifying Angle Relationships Lesson 2-6

Lesson 2-4 2-2 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: 2-2 2-3 2-4 2-5 2-6 2-7 2-8