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H arr y P otter

Sophie Heflin Maile Murphy Erin Dennis. H arr y P otter. Chapter 2 Review: Reasoning and Proof. This Chapter Covers: 2-1: Inductive Reasoning and Conjecture 2-2: Logic 2-3: Conditional Statements 2-4: Deductive Reasoning 2-5: Postulates and Paragraph Proofs 2-6: Algebraic Proof

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H arr y P otter

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  1. Sophie Heflin Maile Murphy Erin Dennis HarryPotter Chapter 2 Review: Reasoning and Proof This Chapter Covers: 2-1: Inductive Reasoning and Conjecture 2-2: Logic 2-3: Conditional Statements 2-4: Deductive Reasoning 2-5: Postulates and Paragraph Proofs 2-6: Algebraic Proof 2-7: Proving Segment Relationships 2-8: Proving Angle Relationships No Spells Allowed

  2. 2-1: Inductive Reasoning and Conjecture Topics Covered: Inductive reasoning: reasoning that uses a number of specific examples to arrive at a conclusion. Conjecture: A concluding statement reached using inductive reasoning. Counterexample: A false example, such as a number, a drawing, or a statement that disproves a conjecture.

  3. 2-2: Logic Topics Covered: Statement: A sentence that is either true or false. Truth value: The truth value of a statement is either true (T) or false (F). Negation: The negation of a statement has the opposite meaning, as well as an opposite truth value. Compound statement: Two or more statements joined by the word and or or. Conjunction: A compound statement using the word and. Disjunction: A compound statement that uses the word or. Truth table: A convenient method for organizing the truth values of statements. Conjunction Truth Table

  4. 2.3-Conditional Statements Conditional Statement-A statement that can be written in if-then form. if-then statement-is the form if p, then q. The Hypothesis-of a conditional statement is the phrase immediately following the word if. The Conclusion-of a conditional statement is the phrase immediately following the word then. Related Conditional-statements based on a given conditional statement. The Converse-is formed by exchanging the hypothesis and conclusion of the conditional. The Inverse-is formed by negating both the hypothesis and conclusion of the conditional. The Contrapositive-is formed by negating both the hypothesis and the conclusion of the conclusion of the converse of the conditional. Logically Equivalent- Statements with the same truth values

  5. 2-4: Deductive Reasoning Deductive Reasoning- A conjecture made using facts, rules, definitions, or properties that reach logical conclusions from given statements. Valid- A conjecture that is logically correct. Law of Detachment- A valid form of deductive reasoning: If p --> q is a true statement and p is true, then q is true. Law of Syllogism- Another valid form of deductive reasoning: If p--> q and q--> r are true statements, then p-->r is a true statement.

  6. 2-5: Postulates Postulate (Axiom): A statement that is accepted as true without proof. Proof: A logical argument in which each statement you make is supported by a statement that is accepted as true. Theorem: A statement or conjecture that has been proven. Deductive argument: a logical chain of statements linking the given to what you are trying to prove.

  7. 2-6: Algebraic Proof Algebraic Proof: A proof that is made up of a series of algebraic statements. Two-column Proof (Formal Proof): A proof that contains statements and reasons organized in two columns.

  8. 2-7: Proving Segment Relationships Segment Addition Postulate: If A, B, and C are collinear, then point B is between A and C if and only if AB + BC = AC Properties of Segment Congruence: Reflexive Property of Congruence: LineAB is congruent to lineAB Symmetric Property of Congruence: If lineAB is congruent to lineCD, then lineCD is congruent to lineAB Transitive Property of Congruence: If lineAB is congruent to lineCD and lineCD is congruent to lineEF, then lineAB is congruent to lineEF.

  9. 2-8: Proving Angle Relationships Topics to know: Angle Addition Postulate Supplement Theorem Complement Theorem Reflexive Property of Congruence Symmetric Property of Congruence Transitive Property of Congruence Congruent Supplements Theorem Congruent Complements Theorem Vertical Angles Theorem Right Angle Theorems

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