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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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### GBK Geometry

Jordan Johnson

• Greeting

• Warm-up / Check HW / Questions

• Lesson: Parallel Lines; the Parallel Postulate

• Homework / Questions

• Clean-up

• 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

• 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.

• 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.

• 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.)

• 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.

• 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.

• 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)

• Pick up all trash / items.

• Push in chairs (at front and back tables).

• See you tomorrow!