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GBK Geometry

GBK Geometry. Jordan Johnson. Today’s plan. Greeting Review Asg #10 Puzzle Questions on reading (2.5)? Lesson : Deductive Systems Homework / Questions Clean-up. Puzzle – Discuss in pairs. – Martin Gardner Scientific American July 1971.

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GBK Geometry

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  1. GBK Geometry Jordan Johnson

  2. Today’s plan • Greeting • Review Asg #10 • Puzzle • Questions on reading (2.5)? • Lesson: Deductive Systems • Homework / Questions • Clean-up

  3. Puzzle – Discuss in pairs – Martin GardnerScientific American July 1971 A boy and a girl are sitting on the front steps of their commune. “I’m a boy,” said the one with black hair. “I’m a girl,” said the one with red hair. If at least one of them is lying, who is which? • Given facts: • One boy, one girl. • The black-haired one says “I’m a boy.” • The red-haired one says “I’m a girl.” • At least one is lying.

  4. Components of a Deductive System • Undefined terms • (to avoid circularity) • Definitions • (to provide facts and convenient names) • Postulates • (to avoid circularity) • Theorems • (proven directly or indirectly by logical rules)

  5. Definitions • Known terms: • Points are collineariff there is a line containing all of them. • Lines are concurrentiff there is a point that they all contain. • New ones: • Postulate – synonym for axiom – a statement we assume to be true.

  6. Postulates • Postulate 1: • Two points determine a line. • Postulate 2: • Three noncollinear points determine a plane. • Here, “determine” means: • There is only one line (or plane) passing through the chosen points.

  7. Work • Read Ch. 2 Lesson 5 (if not already done) and 6. • For tomorrow/Friday: • Asg #11 • Week 6 Journal • For Monday:Asg #12 • Tuesday:Asg #13 • Wednesday: • Asg #14 • Unit 2 Test

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

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