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Exterior Angle Sum of a Polygon

Exterior Angle Sum of a Polygon
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2017-03-02 04:51
PolygonAngleGeometric Construction
This example demonstrates how to dynamically calculate the sum of exterior angles of any polygon. It involves core math concepts like polygons, exterior angles, and angle sums. Construction highlights include using GeoGebra commands: Segment, Translate, Vector, and Angle. Suitable for middle school and above students to understand the theorem and its applications.

GeoGebra Commands & Parameters

  1. Segment(A, B) → f
  2. Segment(B, C) → g
  3. Segment(C, D) → h
  4. Segment(D, E) → i
  5. Segment(E, F) → j
  6. Segment(F, G) → k
  7. Segment(G, H) → l
  8. Segment(H, I) → m
  9. Segment(I, J) → p
  10. Segment(J, K) → q
  11. Translate(V, b) → V'
  12. Vector(V, V') → u_1
  13. Translate(V, c) → V'_1
  14. Vector(V, V'_1) → v_1
  15. Translate(V, d) → V'_2
  16. Vector(V, V'_2) → w_1
  17. Translate(V, e) → V'_3
  18. Vector(V, V'_3) → a_1
  19. Translate(V, r) → V'_4
  20. Vector(V, V'_4) → b_1
  21. Translate(V, s) → V'_5
  22. Vector(V, V'_5) → c_1
  23. Translate(V, t) → V'_6
  24. Vector(V, V'_6) → d_1
  25. Translate(V, u) → V'_7
  26. Vector(V, V'_7) → e_1
  27. Translate(V, v) → V'_8
  28. Vector(V, V'_8) → f_1
  29. Translate(V, w) → V'_9
  30. Vector(V, V'_9) → g_1
  31. Angle(e_1, f_1) → α
  32. Angle(f_1, g_1) → β
  33. Angle(g_1, u_1) → γ
  34. Angle(u_1, v_1) → δ
  35. Angle(v_1, w_1) → ε
  36. Angle(w_1, a_1) → ζ
  37. Angle(a_1, b_1) → η
  38. Angle(b_1, c_1) → θ
  39. Angle(c_1, d_1) → ι
  40. Angle(d_1, e_1) → κ

AI Drawing Prompt Reference

Draw a polygon and dynamically show the sum of its exterior angles. First, create the vertices A, B, C, D, E, F, G, H, I, J, K, then connect these vertices to form the polygon. Next, starting from vertex A, use translation and rotation to construct each exterior angle. Finally, calculate and display the sum of all exterior angles.
The prompt above was compiled from the original drawing commands and is for reference only.