Geometry Lesson 2 2 TODAYS OBJECTIVE Standard MM

Geometry - Lesson 2. 2 TODAY’S OBJECTIVE: Standard: MM 1 G 2 Students will understand use the language of mathematical argument and justification. a. b. Use conjecture, inductive reasoning, deductive reasoning, counterexamples, and indirect proof as appropriate. Understand use the relationships among a statement and its converse, inverse, and contrapositive.

Essential Question OWhat is logic?

Conditionals (If-then form) OConditionals are if-then statements O Ex: If you are fourteen, then you are a teenager. O Ex: If x=10, then 2 x=20.

Converse, Inverse, & Contrapositive O Statement: if p then q O Statement: If you do O Converse: if q then p O Inverse: if not p then not q O Contrapositive: if not q then not p your math homework, then you get a good grade. O Converse: If you get a good grade, then you do your math homework. O Inverse: If you don’t do your math homework, then you don’t get a good grade. O Contrapositive: If you don’t get a good grade, then you don’t do your math homework.

Negation O The negation of statement p is "not p. " O The negation of p is symbolized by "~p. " Now, you try. Negate the following statement: If you can eat something, then it is considered food. Negation: If you cannot eat something, then it is not considered food

Biconditional O A biconditional statement is defined to be true whenever both parts have the same truth value. O The biconditional operator is denoted by a double-headed arrow O The biconditional p . q represents: "p if and only if q, " where p is a hypothesis and q is a conclusion.

Inductive & Deductive Reasoning O Also known as logical reasoning O Systems for reaching logical conclusions Inductive reasoning: the process of arriving at a conclusion based on a set of observations. In itself, it is not a valid method of proof. Deductive reasoning: the process of arriving at a conclusion based on previously known facts. It is the way proofs are written.

Law of Syllogism O The Law of Syllogism: O If and then p → q is true, q → r is true, p r is also true. O Use the Law of Syllogism to come to a conclusion in the following example.

Example: O Given 1: If I study and work hard, then I get good grades. O Given 2: If I get good grades, then I get into a good college. O Therefore: If I study and work hard. . . I get into a good college!

Practice Time! O In the textbook, write answers only! O Do page 207 Set A Odd Numbers. O Do page 209 Set B Even Numbers. O Work in your groups O Raise your hand, for help!