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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

GBK Geometry

Jordan Johnson

today s plan
Today’s plan
  • Greeting
  • Warm-up / Check HW / Questions
  • Lesson: Parallel Lines; the Parallel Postulate
  • Homework / Questions
  • Clean-up
today s plan1
Today’s plan
  • Greeting
  • Tests / Check HW / Warm-up
  • Lesson: Parallel Lines; the Parallel Postulate
  • Homework / Questions
  • Clean-up
grade meanings
Grade meanings
  • “A” = outstandingly good
  • “B” = good enough
  • “C” = minor problems
  • “D” = serious problems
  • “F” = no effort or no idea what’s going on
warm up
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.
parallel lines
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.
the parallel postulate
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.)
the parallel postulate1
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.
additional theorem ch 6 lesson 3
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.
homework
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)
clean up reminders
Clean-up / Reminders
  • Pick up all trash / items.
  • Push in chairs (at front and back tables).
  • See you tomorrow!
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