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Sum of Angles in Two Regular Polygons

Sum of Angles in Two Regular Polygons
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2020-03-29 09:16
PolygonAngleGeometric Construction
This example demonstrates the calculation and visualization of the sum of interior angles in two regular polygons. Key math concepts include the formula for the sum of interior angles of polygons, properties of regular polygons, and angle calculations. Construction highlights involve GeoGebra commands/objects like Intersect (intersection), Point (point), Polygon (polygon), Circle (circle), Line (line), Midpoint (midpoint), Angle (angle), Segment (segment), Rotate (rotation), and CircleSector (sector). Suitable for high school geometry teaching, helping students understand the patterns and calculations of interior angles in regular polygons.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → A
  2. Point(xAxis) → B
  3. Polygon(A, B, 4) → poly1, f, g, h, i, C, D
  4. Circle(D, 1 + a / 2) → e
  5. Circle(D, a) → c
  6. Intersect(c, h, 1) → E
  7. Intersect(e, yAxis, 1) → F
  8. Line(F, E) → j
  9. Midpoint(F, E) → G
  10. Circle(G, 3.5) → d
  11. Intersect(d, j, 1) → H
  12. Intersect(d, j, 2) → I
  13. Polygon(I, H, 3) → poly2, k, l, m, J
  14. Intersect(i, l) → K
  15. Intersect(h, m) → L
  16. Angle(F, K, H) → α
  17. Angle(L, E, I) → β
  18. Angle(D, E, F) → γ
  19. Angle(H, F, K) → δ
  20. Angle(E, F, D) → ε
  21. Angle(I, L, E) → ζ
  22. Angle(J, L, C) → η
  23. Angle(A, K, J) → θ
  24. Angle(K, H, F) → ι
  25. Angle(E, I, L) → κ
  26. Angle(F, D, E) → μ
  27. Circle(M, 1) → p
  28. Point(p) → N
  29. Segment(M, N) → n
  30. Rotate(N, θ, M) → N'
  31. Angle(N, M, N') → ν
  32. Rotate(N', η, M) → N''
  33. Angle(N', M, N'') → ξ
  34. CircleSector(M, N, N') → q
  35. CircleSector(M, N', N'') → r
  36. Ray(N, M) → s
  37. Intersect(p, s, 2) → O
  38. Segment(O, N) → t
  39. Angle(N, M, N'') → ο
  40. Rotate(N, (-(120° - θ)), M) → N'_1
  41. Angle(N'_1, M, N) → ρ
  42. Rotate(N'', 120° - η, M) → N'''
  43. Angle(N'', M, N''') → σ
  44. CircleSector(M, N'_1, N) → c_1
  45. CircleSector(M, N'', N''') → d_1
  46. Ray(N', M) → b
  47. Intersect(p, b, 2) → P
  48. CircleSector(M, N''', P) → e_1
  49. CircleSector(M, P, N'_1) → f_1