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四边形内角和与外角和定理演示

四边形内角和与外角和定理演示
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2015-10-22 22:41
多边形角几何作图滑块动画
所属专题 Polygons & Angles Polygons & Angles Polygons & Angles ( s n attar) Polygons & Angles Polygons & Angles Polygons & Angles Polygons & Angles Geometry: Polygons & Angles Geometry: Polygons & Angles
①本范例通过交互式演示，向学生展示任意四边形的内角和为360度，以及外角和的性质。②涉及的核心数学概念包括多边形内角和定理、外角和定理、角度测量。③作图要点：使用了GeoGebra命令如Ray, Point, Circle, Intersect, Segment, Angle, CircleSector, Vector, Translate, Dilate, Rotate, Mirror, Line, Polygon等来构建四边形及其内外角。④适合初中及以上数学学习者，用于直观理解四边形角度性质，增强空间想象能力。

GeoGebra 命令及参数

  1. Ray(P, A) → h_1
  2. Point(h_1) → R
  3. Ray(A, R) → j_1
  4. Ray(A, B) → a
  5. Circle(A, 1.5) → g
  6. Intersect(g, j_1) → I_1,
  7. Intersect(g, a, 1) → H
  8. Segment(P, A) → l_1
  9. Intersect(g, l_1, 1) → H_1
  10. Segment(P, C) → k_1
  11. Circle(C, 1.5) → k
  12. Intersect(k, k_1) → Z,
  13. Ray(B, C) → b
  14. Intersect(k, b) → M, N
  15. Ray(C, A) → c
  16. Point(a) → D_1
  17. Point(b) → E_1
  18. Point(c) → F_1
  19. Ray(A, F_1) → d
  20. Ray(B, D_1) → e
  21. Ray(C, E_1) → f
  22. Point(e) → D
  23. Point(f) → E
  24. Angle(C, B, A) → β
  25. Angle(A, C, B) → γ
  26. Angle(D, B, C) → ε
  27. Angle(E, C, A) → ζ
  28. Circle(B, 1.5) → h
  29. Intersect(g, c, 1) → G
  30. Intersect(g, c, 2) → I
  31. Intersect(h, b, 1) → J
  32. Intersect(h, a, 1) → K
  33. Intersect(h, a, 2) → L
  34. Intersect(k, c) → O,
  35. CircleSector(C, Z, M) → r
  36. CircleSector(B, J, K) → q
  37. CircleSector(B, L, J) → t
  38. Vector(B, C) → u
  39. CircleSector(A, I_1, H) → c_1
  40. Vector(A, C) → v
  41. Translate(q, u) → q'
  42. Segment(B, C) → l
  43. Dilate(C, If[0 < j ≤ 1, j, 0], B) → C'
  44. Vector(B, C') → w
  45. Translate(q, w) → q'_1
  46. Rotate(q'_1, If[0 < j, (((-j) * 180))°, 180*°], C') → d_1
  47. Mirror(q', C) → q''
  48. Dilate(A, If[1 < j ≤ 2, 2 - j, 0], C) → C'_1
  49. Vector(A, C'_1) → m
  50. CircleSector(A, H, H_1) → p
  51. Translate(p, m) → p'
  52. Dilate(C, If[0 < n ≤ 1, n, 0], B) → C'_2
  53. Dilate(A, If[1 < n ≤ 2, 2 - n, 0], C) → A'
  54. Vector(B, C'_2) → u_1
  55. Vector(A, A') → v_1
  56. If(0 < n ≤ 1, Translate[t, u_1], Translate[t, u]) → e_1
  57. If(1 < n ≤ 2, Translate[c_1, v_1], Translate[c_1, v]) → f_1
  58. Ray(C, P) → g_1
  59. Point(g_1) → Q
  60. Ray(P, Q) → i_1
  61. Point(i_1) → S
  62. Point(j_1) → T
  63. Circle(P, 1.5) → p_1
  64. Intersect(p_1, l_1) → U,
  65. Intersect(p_1, i_1) → V,
  66. Intersect(p_1, k_1) → W,
  67. CircleSector(P, U, W) → q_1
  68. Intersect(k, b, 2) → A_1
  69. Intersect(k, r, 1) → B_1
  70. Line(P, b) → b_1
  71. Intersect(p_1, b_1) → C_1, G_1
  72. Angle(B, A, P) → α
  73. Vector(P, C) → i
  74. Rotate(p', If[1 < j ≤ 2, 0*°, 0*°], C'_1) → p''
  75. Dilate(P, If[2 < j ≤ 3, 3 - j, 0], C) → P'
  76. Vector(P, P') → w_1
  77. Translate(q_1, w_1) → r_1
  78. Rotate(r_1, If[2 < j ≤ 3, (((j - 2) * 180))°, 180*°], P') → s_1
  79. CircleSector(C, N, Z) → s
  80. CircleSector(P, V, U) → t_1
  81. Dilate(P, If[2 < n ≤ 3, 3 - n, 0], C) → P'_1
  82. Vector(P, P'_1) → m_1
  83. If(2 < n ≤ 3, Translate[t_1, m_1], Translate[t_1, w_1]) → e_2
  84. Angle(H, A, I_1) → δ
  85. Angle(V, P, U) → η
  86. Angle(U, P, W) → θ
  87. Polygon(A, B, C, P) → poly1, a_2, b_2, c_2, p_2