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GBK Geometry

Today's lesson focuses on polygons, defined as a collection of at least three line segments that form a closed shape. We will review previous definitions and clarify what qualifies as a polygon. Students will sketch examples and non-examples to solidify their understanding. Homework includes exercises from Chapter 4, Lesson 2, with various problems due on specific dates. Remember to clean up after class and submit your journals as well. Let’s ensure we understand polygons before moving on to more complex shapes!

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GBK Geometry

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  1. GBK Geometry Jordan Johnson

  2. Today’s plan • Greeting • Warm-up & Puzzle • Lesson: Polygons • Homework / Questions • Clean-up

  3. Reptiles as Polygons – M.C. Escher

  4. From paper to paving

  5. Polygons • Again? Didn’t we define them already? • Our previous definition:

  6. Polygons • Again? Didn’t we define them already? • Our previous definition: • A mumble mumblemumblemumblebounded by mumble mumblemumblemumble.

  7. Polygons • Again? Didn’t we define them already? • Our previous definition: • A 2-D figure bounded by line segments.

  8. Polygons • Again? Didn’t we define them already? • Our previous definition: • A 2-D figure bounded by line segments.

  9. Polygons • Again? Didn’t we define them already? • Our previous definition: • A 2-D figure bounded by line segments.

  10. Polygons • OK…here’s the “official” definition from the book: • A polygonis a connected set of at least three line segments in the same plane, such that each segment intersects exactly two others, one at each endpoint. • Why so complicated? • Avoid self-crossing polygons. • Avoid using terms we haven’t defined. • Break the definition down into isolated facts.

  11. Examples and Non-Examples • Sketch 2 example polygons that fit our definition. • Sketch figures that fail to be polygons, in these ways: • Have “sides” that aren’t line segments. • Have fewer than 3 line segments. • Aren’t entirely contained in one plane. • Have segments intersecting more than 2 others. • Have segments intersecting at points other than their endpoints.

  12. Polygons • The bounding segments are sides. • The sides’ intersections are vertices. • Abbreviating polygon names: name the vertices in order. • For example,“Polygon ABCDE”:

  13. Polygons • Name the vertices of the two polygons you drew earlier. • Write the name of each polygon. • (Use its side-based name, e.g. “pentagon PQRST”, if you can.)

  14. Assignments • Asg #27: From Ch. 4 Lesson 2 (pp. 141-144): • Exercises #1-7, 20-24, 37-54. • Bonus: Set III • Due Thursday, 11/7 (per. 1-2) or Friday, 11/8 (7). • Journal #9 – also due Thu/Fri. • Unit 3 Test Corrections – due Tuesday, 11/13. • Center of the circle?

  15. Puzzle Find the center.

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

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