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GBK Geometry

GBK Geometry. Jordan Johnson. Today’s plan. Greeting Converse of the Pythagorean Theorem Review Homework Lesson: Homework / Questions Clean-up. Converse of the Pythagorean Thm . What is the converse of the Pythagorean Theorem?

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GBK Geometry

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  1. GBK Geometry Jordan Johnson

  2. Today’s plan • Greeting • Converse of the Pythagorean Theorem • Review Homework • Lesson: • Homework / Questions • Clean-up

  3. Converse of the Pythagorean Thm. • What is the converse of the Pythagorean Theorem? • In a triangle ΔABC with side lengths a, b, and c(where c > a and c > b), if a2 + b2 = c2, then ΔABC is a right triangle.

  4. Converse of the Pythagorean Thm. • If… • a2 + b2 < c2 • a2 + b2= c2 • a2 + b2> c2 • …then ΔABC is… • obtuse • right • acute

  5. Pythagorean Theorem:Alternate Proof Write-up • 5 minutes: Read the proof. • How is the new proof different from the old? • In what ways is it clearer? • Or less clear? • In what ways is it simpler? • Or more complicated? • What different techniques do the new & old versions use?

  6. Proof Evaluation • Simplicity. Which proof is simpler? Which is more complex? Where does the complexity come from? • Clarity. Which proofs are easiest to understand? Are the simpler ones easier to understand? If not, why? What techniques do the various proofs use to help the reader understand? • Instructive value, in general. What can we learn from each of the four proofs? What mathematical techniques do they all have in common? What mathematical concepts distinguish each of them from the others? • Instructive value, personal to you. You will likely find that you understand some proofs better than others. What does this suggest about your own current knowledge of geometry? Which concepts are most familiar and comfortable to you? Which are least familiar? • Visual appeal. Which proofs use a more visually pleasing technique? Which proofs have diagrams that make the most sense to you visually? • Creativity. Which proofs have ideas that were surprising and novel to you?

  7. Work • Now: • Do Asg #63 and/or #64. • Tonight’s 25+ minutes: • Read more of the proofs, and write down observations you may use in your paper.

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

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