1 / 9

GBK Geometry

GBK Geometry. Jordan Johnson. Today’s plan. Greeting Unit 1 Review / Practice Quiz Lesson: Indirect Proof Homework / Questions Clean-up. Card Tricks. For this exercise, speak only when called on. Split into two groups: one against the front wall one against the back wall

selina
Download Presentation

GBK Geometry

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. GBK Geometry Jordan Johnson

  2. Today’s plan • Greeting • Unit 1 Review / Practice Quiz • Lesson: Indirect Proof • Homework / Questions • Clean-up

  3. Card Tricks • For this exercise, speak only when called on. • Split into two groups: • one against the front wall • one against the back wall • One volunteer from each group, step forward.

  4. Indirect Proof Prove X. Original problem: i.e., prove that the opposite leads to a contradiction Prove the opposite of X is impossible. New problem:

  5. Example How did we prove the checker-board tiling was impossible? • Suppose we could tile the board. • If we can, then every domino covers a white and a black square. • Thus we’d always cover the same number of white and black squares. • There are 30 white & 32 black squares, contradicting statement #3.

  6. 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.

  7. Practice problem – A Poker Proof • Theorem: • If I hold this hand,nobody holds a royal flush. • What’s our initial assumption? • What’s our reasoning? • What contradiction do we reach?

  8. Work • Write up today’s lesson in your journal. • For tomorrow: Unit 1 Test Analysis • For Wednesday:Asg #10 • For Thursday/Friday: • Asg #11 • Week 6 Journal

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

More Related