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GBK Geometry

GBK Geometry. Jordan Johnson. Today’s plan. Greeting Not-a-Quiz Mini-Lesson: Parallel Line Theorems Homework / Questions Clean-up. Practice Quiz. Answer in complete sentences: State the Parallel Postulate. Why is the Parallel Postulate historically significant?

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GBK Geometry

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  1. GBK Geometry Jordan Johnson

  2. Today’s plan • Greeting • Not-a-Quiz • Mini-Lesson: Parallel Line Theorems • Homework / Questions • Clean-up

  3. Practice Quiz • Answer in complete sentences: • State the Parallel Postulate. • Why is the Parallel Postulate historically significant? • What do you get if you assume the Parallel Postulate is false?

  4. Practice Quiz: Answers • Answer in complete sentences: • State the Parallel Postulate. • Through a given point P not on a line m, there is exactly one line parallel to m. • Why is the Parallel Postulate historically significant? • Mathematicians tried to prove it for thousands of years, and eventually discovered (in the 1800s) that it cannot be proven – and that other types of geometry than Euclid’s are possible. • What do you get if you assume the Parallel Postulate is false? • You get a different kind of geometry, such as geometry on a sphere’s surface.

  5. Ch. 6, Lessons 2 & 4Parallel Line Theorems • Thm. 17: • equal corresponding angles  parallel lines • Cor. 1: equal alt. int. angles  parallel lines • Cor. 2: supplementary same side int. angles  parallel lines • Cor. 3: Two lines in a plane perpendicular to a third  parallel lines • Thm. 19: • parallel lines  equal corr. angles • … • 19 and its corollaries are converses of 17 and its corollaries.

  6. Lab • Take HW; log it if you haven’t already. • Problems with online HW log? Let me know. • Identify two proof problems you’ll write over the next week. • Do the parallel-line-through-point construction in GeoGebra. • Options: • Constructions in GeoGebra • Khan Academy – Inequalities / Parallel Lines • Week 22 Journal

  7. Homework • Log 25 minutes (online): • Asgs #43-45 (Ch. 6 Lessons 1-3) • Proof work: • Theorem 16 – points equidistant from A and B determine the perp. bisector of AB • Converse of 16 – all points on the perp. bisector of AB are equidistant from the ends of AB • Theorem 17 – prove by contradiction, or study & rewrite the proof on p. 220 • Corollaries to Thm. 17 (see p. 220)

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

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