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GBK Geometry

GBK Geometry. Jordan Johnson. Today’s plan. Greeting Review Asg #11: From Ch . 2, L. 3 (pp. 52-54): Set I: 1-16, 19-20. Set II: 22-28. Bonus: Set III: 1-2 Lesson : Indirect Proof Homework / Questions Clean-up. Indirect Proof / Contradiction. Alternative to direct proof:

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GBK Geometry

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  1. GBK Geometry Jordan Johnson

  2. Today’s plan • Greeting • Review Asg #11: From Ch. 2, L. 3 (pp. 52-54): • Set I: 1-16, 19-20. • Set II: 22-28. • Bonus: Set III: 1-2 • Lesson: Indirect Proof • Homework / Questions • Clean-up

  3. Indirect Proof / Contradiction • Alternative to direct proof: • Start by assuming the opposite of the conclusion you want, and prove that it leads to a contradiction. • If you want to prove (a c)… • Assume that a holds • Assume that (not c) holds • See if you can come up with a contradiction.

  4. Example Our “checkerboard proof” was a proof by contradiction: • Assume you can tile the board. • If you can do it, then every domino covers a white and a black square. • Therefore, the same number of white and black squares are covered. • There are 30 white & 32 black squares, contradicting statement #3.

  5. Practice problem – A Poker Proof • Theorem: • In this deal of the cards,nobody holds a royal flush. • What’s our initial assumption? • What’s our reasoning? • What contradiction do we reach?

  6. Homework • Asg #12: Read Chapter 2, Lesson 4, pp. 55-59, and do: • Set I: Exercises 1-5, 9-14. • Set II: Exercises 16 and 18-21. • Bonus: Set III. • Due Friday, 9/28. • Journal #4 – due Friday. • Test Corrections: • Name/date/period on a separate sheet of paper • Divide the sheet into 2 sections: • careless mistakes • things you didn’t understand • Write correct answers and explanations. • Due Friday, 9/28. • Read Chapter 2, Lesson 5 (pp. 60-61). • In your notes, record italicized terms. • In a separate section of your notes, record postulates. • Asg #13: From Ch. 2, Lesson 5 (pp. 61-64), do: • Set I Exercises #1-3, 6-18. • Set II Exercises #32-41. • Bonus: Set III. • Due Monday.

  7. Clean-up / Reminders • Pick up all trash / items. • Push in chairs (at front and back tables). • See you tomorrow!

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