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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
- Clean-up

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

- 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

- 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

- 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 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:

- 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

- 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

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

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