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GBK Geometry

GBK Geometry. Jordan Johnson. Today’s plan. Greeting Warm-up / Check HW / Questions Lesson: Parallel Lines; the Parallel Postulate Homework / Questions Clean-up. Today’s plan. Greeting Tests / Check HW / Warm-up Lesson: Parallel Lines; the Parallel Postulate Homework / Questions

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GBK Geometry

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  1. GBK Geometry Jordan Johnson

  2. Today’s plan • Greeting • Warm-up / Check HW / Questions • Lesson: Parallel Lines; the Parallel Postulate • Homework / Questions • Clean-up

  3. Today’s plan • Greeting • Tests / Check HW / Warm-up • Lesson: Parallel Lines; the Parallel Postulate • Homework / Questions • Clean-up

  4. Grade meanings • “A” = outstandingly good • “B” = good enough • “C” = minor problems • “D” = serious problems • “F” = no effort or no idea what’s going on

  5. Warm-up • Sketch a triangle. Name all its interior and exterior angles with numbers (e.g. 1, 2, …). • How many angles are not labeled, now? • Write one inequality that relates an exterior angle to a remote interior angle.

  6. Parallel Lines • Construction: • Draw a line and label it m. • Draw a point P that’s not on line m. • In a different color, construct a line m′ that is parallel to m and passes through P.

  7. The Parallel Postulate • Through a point not on a line, there is exactly one line parallel to the given line. • Symbolically: • Given line AB and point P, there is exactly one line parallel to AB passing through P. • (Exactlymeans both at least and no more than.)

  8. The Parallel Postulate • Given line AB and point P, there is exactly one line parallel to AB passing through P. • Long history: • Euclid couldn’t prove it. • Hundreds of other mathematicians tried to prove it. • Geometry works OK with or without it.

  9. Additional theorem – Ch. 6 Lesson 3: • In a plane, two lines parallel to a third line are parallel to each other. • Formally: • For all lines l, m, and n, if l║m and m║n, then l║n. • In other words, parallelism is transitive. • Proof is in the homework.

  10. 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)

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

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