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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!