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Exploring the Sum of Exterior Angles of a Polygon

Exploring the Sum of Exterior Angles of a Polygon
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2022-11-19 04:05
PolygonAngleCoordinate GeometryGeometric ConstructionSlider Animation
This example dynamically demonstrates the exterior angles of a polygon to help students understand the sum of exterior angles. Key mathematical concepts include the exterior angle sum theorem. GeoGebra commands used include Polygon, DynamicCoordinates, PointToPixels, etc. Suitable for middle school grades 6-8 to explore problems related to the interior and exterior angles of convex polygons.

GeoGebra Commands & Parameters

  1. Polygon({(left, bottom), (left, top), (right, top), (right, bottom)}) → viewbox
  2. DynamicCoordinates(A71, If[D71, x(A71), x(C71)], If[D71, y(A71), y(C71)]) → B71
  3. PointToPixels(Corner[1], Corner[3], Corner[5], B71) → StartPointPixels
  4. DynamicCoordinates(A31, If[D31, x(A31), x(C31)], If[D31, y(A31), y(C31)]) → B31
  5. DynamicCoordinates(A32, If[D32, x(A32), x(C32)], If[D32, y(A32), y(C32)]) → B32
  6. DynamicCoordinates(A33, If[D33, x(A33), x(C33)], If[D33, y(A33), y(C33)]) → B33
  7. DynamicCoordinates(A29, If[D29, x(A29), x(C29)], If[D29, y(A29), y(C29)]) → B29
  8. DynamicCoordinates(A30, If[D30, x(A30), x(C30)], If[D30, y(A30), y(C30)]) → B30
  9. DynamicCoordinates(A34, If[D34, x(A34), x(C34)], If[D34, y(A34), y(C34)]) → B34
  10. DynamicCoordinates(A35, If[D35, x(A35), x(C35)], If[D35, y(A35), y(C35)]) → B35
  11. DynamicCoordinates(A36, If[D36, x(A36), x(C36)], If[D36, y(A36), y(C36)]) → B36
  12. DynamicCoordinates(A39, If[D39, x(A39), x(C39)], If[D39, y(A39), y(C39)]) → B39
  13. DynamicCoordinates(A40, If[D40, x(A40), x(C40)], If[D40, y(A40), y(C40)]) → B40
  14. DynamicCoordinates(A41, If[D41, x(A41), x(C41)], If[D41, y(A41), y(C41)]) → B41
  15. DynamicCoordinates(A42, If[D42, x(A42), x(C42)], If[D42, y(A42), y(C42)]) → B42
  16. DynamicCoordinates(A43, If[D43, x(A43), x(C43)], If[D43, y(A43), y(C43)]) → B43
  17. DynamicCoordinates(A44, If[D44, x(A44), x(C44)], If[D44, y(A44), y(C44)]) → B44
  18. DynamicCoordinates(A45, If[D45, x(A45), x(C45)], If[D45, y(A45), y(C45)]) → B45
  19. DynamicCoordinates(A49, If[D49, x(A49), x(C49)], If[D49, y(A49), y(C49)]) → B49
  20. DynamicCoordinates(A50, If[D50, x(A50), x(C50)], If[D50, y(A50), y(C50)]) → B50
  21. DynamicCoordinates(A51, If[D51, x(A51), x(C51)], If[D51, y(A51), y(C51)]) → B51
  22. DynamicCoordinates(A52, If[D52, x(A52), x(C52)], If[D52, y(A52), y(C52)]) → B52
  23. DynamicCoordinates(A53, If[D53, x(A53), x(C53)], If[D53, y(A53), y(C53)]) → B53
  24. DynamicCoordinates(A57, If[D57, x(A57), x(C57)], If[D57, y(A57), y(C57)]) → B57
  25. DynamicCoordinates(A58, If[D58, x(A58), x(C58)], If[D58, y(A58), y(C58)]) → B58
  26. DynamicCoordinates(A59, If[D59, x(A59), x(C59)], If[D59, y(A59), y(C59)]) → B59
  27. DynamicCoordinates(A60, If[D60, x(A60), x(C60)], If[D60, y(A60), y(C60)]) → B60
  28. DynamicCoordinates(A61, If[D61, x(A61), x(C61)], If[D61, y(A61), y(C61)]) → B61
  29. DynamicCoordinates(A64, If[D64, x(A64), x(C64)], If[D64, y(A64), y(C64)]) → B64
  30. DynamicCoordinates(A65, If[D65, x(A65), x(C65)], If[D65, y(A65), y(C65)]) → B65
  31. DynamicCoordinates(A66, If[D66, x(A66), x(C66)], If[D66, y(A66), y(C66)]) → B66
  32. DynamicCoordinates(A67, If[D67, x(A67), x(C67)], If[D67, y(A67), y(C67)]) → B67
  33. DynamicCoordinates(A54, If[D54, x(A54), x(C54)], If[D54, y(A54), y(C54)]) → B54
  34. Polygon(C29:C36) → B28
  35. Polygon(C39:C45) → B38
  36. Sum(H29:H34) → test
  37. Polygon(C49:C54) → B48
  38. Polygon(C57:C61) → B56
  39. Polygon(C64:C67) → B63
  40. Zip(CircleSector[A, B, C], A, {B64, B65, B66, B67}, B, {E64, E65, E66, E67}, C, {B65, B66, B67, B64}) → SectorsQuad
  41. Zip(CircleSector[A, B, C], A, B57:B61, B, E57:E61, C, Append[E58:E61, E57]) → SectorsPentagon
  42. Zip(CircleSector[A, B, C], A, B49:B54, B, E49:E54, C, Append[E50:E54, E49]) → SectorsHexagon
  43. Zip(CircleSector[A, B, C], A, B39:B45, B, E39:E45, C, Append[E40:E45, E39]) → SectorsHeptagon
  44. Zip(CircleSector[A, B, C], A, B29:B36, B, E29:E36, C, Append[E30:E36, E29]) → SectorsOctagon
  45. DynamicCoordinates(A70, If[D70, x(A70), x(C70)], If[D70, y(A70), y(C70)]) → B70
  46. DynamicCoordinates(A72, If[D72, x(A72), x(C72)], If[D72, y(A72), y(C72)]) → B72
  47. Zip(CircleSector[A, B, C], A, B70:B72, B, E70:E72, C, {B71, B72, B70}) → SectorsTriangle
  48. Element({SectorsTriangle, SectorsQuad, SectorsPentagon, SectorsHexagon, SectorsHeptagon, SectorsOctagon}, numSides - 2) → currentSectors
  49. Element({B70:B72, B64:B67, B57:B61, B49:B54, B39:B45, B29:B36}, numSides - 2) → currentVertices
  50. Polygon(C70:C72) → B69
  51. Zip(Translate[A, Vector[(slider2 * Vector[B, CircCenter])]], A, currentSectors, B, currentVertices) → moveSectors
  52. Join({B29:B36, B39:B45, B49:B54, B57:B61, B64:B67, B70:B72, {numSides, slider2}}) → tabOrderSaveForLater
  53. onboardingTextOffset(Corner[onboardingText, 1], Corner[onboardingText, 3], 1, Corner[1], Corner[3], Corner[5]) → OnboardingTextOffset
  54. circlePixels(B71, 7 + (7 * pulsing), Corner[1], Corner[3], Corner[5]) → pulsingObject

AI Drawing Prompt Reference

Draw a polygon and dynamically demonstrate the sum of its exterior angles. Start by sketching a quadrilateral, then add vertices to increase the number of sides up to an octagon. At each vertex, draw the corresponding exterior angle with distinct colors. Use a slider to adjust the number of sides, updating the angles and their sum in real-time. Label each exterior angle and display the total sum next to it to verify the exterior angle sum theorem.
The prompt above was compiled from the original drawing commands and is for reference only.