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Your warm up is on the back table.

Your warm up is on the back table. Enjoy!. Before we begin today’s lesson, let’s talk briefly about syllogisms. 3 part logical argument. Syllogism: A three part argument where a set of statements called premises, lead to one logical conclusion. If the premises are true,

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Your warm up is on the back table.

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  1. Your warm up is on the back table. Enjoy!

  2. Before we begin today’s lesson, let’s talk briefly about syllogisms. 3 part logical argument

  3. Syllogism:A three part argument where a set of statements called premises, lead to one logical conclusion. If the premises are true, (and we assume they are), then the conclusion must be true.

  4. Law of Syllogism Behold: this symbol means therefore

  5. If a figure is a rectangle, then it is a parallelogram. If a figure is a parallelogram, then its diagonals bisect each other. If a figure is a rectangle, then its diagonals bisect each other. If a figure is a rectangle, then it is a parallelogram. If a figure is a parallelogram, then its diagonals bisect each other.

  6. Law of Detachment

  7. If a figure is a rectangle, then it is a parallelogram. ABCD is a rectangle. __________________________

  8. If a figure is a rectangle, then it is a parallelogram. ABCD is a rectangle. __________________________

  9. If a figure is a rectangle, then it is a parallelogram. ABCD is a rectangle. __________________________ ABCD is a parallelogram.

  10. 2.1, 2.3, 2.4Inductive and Deductive ReasoningandBiconditional Statements

  11. In order for a TRUE biconditional to be created, the conditional and converse of a statement must be TRUE. Biconditional Statementsare definitions Behold: Conditional: If it is a square then it has four right angles and four congruent sides. Is this true? Converse: If it has four right angles and four congruent sides then it is a square. Is this true? YES! YES!

  12. Converse: If it has four right angles and four congruent sides then it is a square. Since they are both TRUE, we have permission to write a biconditional. Conditional: If it is a square then it has four right angles and four congruent sides. Here’s your rules: Drop the ‘if’ and ‘then’. Connect the hypothesis and conclusion with ‘if and only if’. It is a square IF AND ONLY IF it has four right angles and four congruent sides.

  13. conditional If it is an equilateral triangle, then all of the sides have the same measure. Let’s do it again… If all the sides have the same measure, then it is an equilateral triangle. converse It is an equilateral triangle if and only if all of the sides have the same measure. biconditional WOW!! Look at you!!

  14. ♥A biconditional is a definition. ♥ It can be read frontwards and backwards and be true. ♥ Notation: p q ♥ Abbreviation for ‘if and only if’ = iff

  15. Reasoning based on patterns you have observed. Inductive Reasoning Figure # + 2 = # of sides Find the pattern: • 1. How many sides does the fifth figureof Sequence A have? 2. How many sides does the tenth figure of Sequence A have? 3. How many sides does the fourteenth figure of Sequence A have? 7 12 16

  16. Conjecture = Guess Generally, a guess based on past experience(inductive reasoning)

  17. Deductive Reasoning Law of Detachment: If the hypothesis of a true conditional is true, then the conclusion is true. If pq is true And p is true Then q is true Let’s look in your book – pg 114. Law of Syllogism: Allows you to state a conclusion from two true conditional statements when the conclusion of one statement is the hypothesis of the other statement. If pq is true And q r is true Then pr is true Let’s look in your book – pg 115 and 116.

  18. Let’s play that money game! • If the conditional and converse are true, what do you have permission to make? • What is the notation for a biconditional statement? • Create a biconditional statement: If it is a line segment then it is a piece of a line with two endpoints. • What is inductive reasoning? • What is deductive reasoning? • What is the Law of Detachment? • What is the Law of Syllogism? • What conclusion can you draw from the following statements? If it’s Monday, then it’s meatloaf. It’s Monday. • What law does the previous statement demonstrate? • What conclusion can you draw from the following statements? If it’s ballet, then it’s beautiful. If it’s dancing, then it’s beautiful. • What law does the previous question demonstrate?

  19. ♥Your assignment ♥2.3 and 2.4 Practice Worksheets

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