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Polygon Interior and Exterior Angle Sum Exploration

Polygon Interior and Exterior Angle Sum Exploration
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2019-12-16 23:24
PolygonAngleGeometric Construction
This example dynamically demonstrates the sum of interior and exterior angles theorems for polygons from triangle to octagon. It involves core math concepts like polygon angle sum theorem, exterior angle theorem, and angle measurement. Construction highlights include commands like Segment, Polygon, Angle, Circle from GeoGebra, suitable for middle school and above mathematics education to visually understand polygon angle properties.

GeoGebra Commands & Parameters

  1. Segment(B, C) → e
  2. Segment(C, A) → f
  3. Min(f, e) → m
  4. Segment(A, B) → d
  5. Min(d, f) → o
  6. Min(m, o) → u
  7. Polygon(A, B, C) → poly1, c, a, b
  8. Ray(A, B) → h
  9. Ray(B, C) → i
  10. Ray(C, A) → j
  11. Circle(C, (0.25 * u)) → p
  12. Circle(A, (0.25 * u)) → q
  13. Circle(B, (0.25 * u)) → r
  14. Intersect(p, f) → D,
  15. Intersect(p, e, 1) → E
  16. Intersect(r, e, 1) → F
  17. Intersect(r, d, 1) → G
  18. Intersect(q, d, 1) → H
  19. Intersect(q, f, 1) → I
  20. Intersect(r, h, 2) → J
  21. Intersect(q, j, 2) → K
  22. Intersect(p, i, 2) → L
  23. Midpoint(f) → M
  24. Midpoint(e) → N
  25. CircleSector(A, H, I) → s
  26. CircleSector(B, F, G) → t
  27. CircleSector(C, D, E) → c_1
  28. Angle(A, C, B) → α
  29. CircleSector(C, E, D) → d_1
  30. CircleSector(A, I, H) → e_1
  31. CircleSector(B, G, F) → f_1
  32. Min(d, e) → n
  33. Rotate(s, If[0 < l ≤ 1, (((-l) * 180))°, (-(180°))], M) → s'
  34. Rotate(A, If[0 < l ≤ 1, (((-l) * 180))°, (-(180°))], M) → A'
  35. Segment(M, A') → a_1
  36. Rotate(H, (-(180°)), M) → H'
  37. Line(H', C) → b_1
  38. Rotate(B, If[0 < l ≤ 1, ((l * 180))°, 180°], N) → B'
  39. Rotate(t, If[0 < l ≤ 1, ((l * 180))°, 180°], N) → t'
  40. Segment(N, B') → g_1
  41. Segment(C, M) → h_1
  42. Segment(M, A) → i_1
  43. Segment(C, N) → j_1
  44. Segment(N, B) → k_1
  45. Rotate(A, If[0 < l ≤ 1, ((l * 180))°, (-(180°))], M) → A'_1
  46. Rotate(B, If[0 < l ≤ 1, (((-l) * 180))°, (-(180°))], N) → B'_1
  47. Segment(N, B'_1) → l_1
  48. Segment(M, A'_1) → m_1
  49. Rotate(e_1, If[0 < l ≤ 1, ((l * 180))°, (-(180°))], M) → p_1
  50. Rotate(f_1, If[0 < l ≤ 1, (((-l) * 180))°, (-(180°))], N) → q_1
  51. CircleSector(C, L, D) → r_1
  52. CircleSector(A, K, H) → s_1
  53. CircleSector(B, J, F) → t_1
  54. CircleSector(A, H, K) → c_2
  55. CircleSector(B, F, J) → d_2
  56. CircleSector(C, D, L) → e_2
  57. Dilate(A, 1 - v, C) → A'_2
  58. Dilate(B, 1 - v, C) → B'_2
  59. Vector(A, A'_2) → w
  60. Vector(B, B'_2) → u_1
  61. Translate(s_1, w) → f_2
  62. CircleArc(A, K, H) → g_2
  63. Translate(t_1, u_1) → h_2
  64. CircleArc(B, J, F) → k_2
  65. Translate(c_2, w) → p_2
  66. CircleArc(A, H, K) → q_2
  67. Translate(d_2, u_1) → r_2
  68. CircleArc(B, F, J) → s_2