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TODAY ’ S OBJECTIVE:

Geometry - Lesson 2.2. TODAY ’ S OBJECTIVE:. Standard: MM1G2 Students will understand and use the language of mathematical argument and justification. Use conjecture, inductive reasoning, deductive reasoning, counterexamples, and indirect proof as appropriate.

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TODAY ’ S OBJECTIVE:

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  1. Geometry - Lesson 2.2 TODAY’S OBJECTIVE: Standard: MM1G2 Students will understand and use the language of mathematical argument and justification. Use conjecture, inductive reasoning, deductive reasoning, counterexamples, and indirect proof as appropriate. Understand and use the relationships among a statement and its converse, inverse, and contrapositive.

  2. Warm-Up • Take a look at what we will be doing this unit:

  3. Essential Question • What is logic?

  4. Conditionals (If-then form) • Conditionals are if-thenstatements • Ex: If you are fourteen, then you are a teenager. • Ex: If x=10, then 2x=20.

  5. Converse, Inverse, & Contrapositive • Statement: if p then q • Converse: if q then p • Inverse: if notp then notq • Contrapositive: if notq then notp • Statement: If you do your math homework, then you get a good grade. • Converse: If you get a good grade, then you do your math homework. • Inverse: If you don’tdo your math homework, then you don’tget a good grade. • Contrapositive: If you don’tget a good grade, then you don’t do your math homework.

  6. Negation • The negation of statement p is "not p."  • The negation of p is symbolized by "~p." • Negate a Conditional: (negating IF ... THEN) If you can eat something, then it is considered food. Negation: You eat something AND it is not considered food.

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

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

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

  10. Counter-Example

  11. Practice Time!

  12. Homework:

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