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Exploring Polygons: Definitions, Examples, and Homework Tasks

Today's geometry lesson focuses on polygons, including their definition and properties. Begin with a warm-up task that involves calculating distances between points and a puzzle to locate the center of geometric shapes. We will revisit what defines a polygon, discussing examples and non-examples while emphasizing the importance of avoiding self-crossing figures. You'll practice sketching and naming various polygons, concluding with assigned homework. Remember to tidy up after the lesson. Let's dive into the fascinating world of 2-D shapes!

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Exploring Polygons: Definitions, Examples, and Homework Tasks

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Presentation Transcript

  1. GBK Geometry Jordan Johnson

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

  3. Warm-up Your warm-up task:Find the exact distance between each pair of points. A puzzle:Find the center.

  4. Reptiles as Polygons – M.C. Escher

  5. From paper to paving

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

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

  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 • Our previous definition: • A 2-D figure bounded by line segments.

  11. 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.

  12. 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.

  13. Polygons • The bounding segments are __________.

  14. Polygons • The bounding segments are sides. • The sides’ intersections are ____________.

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

  16. 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.)

  17. Homework • For tomorrow: Asg #25 • For Thursday/Friday:Asg #26

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

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