GBK Geometry

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# GBK Geometry - PowerPoint PPT Presentation

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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Presentation Transcript

### 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
• “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!