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五边形外角探索

五边形外角探索
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2017-06-15 08:16
多边形角几何作图
所属专题 Congruence (CO) Cluster Congruence (Vol 2) Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 Gail LeBlancCCSS High School: Geometry (Congruence) Volume 2 Polygons & Angles Polygons & Angles Polygons & Angles ( s n attar) Polygons & Angles
①本范例演示五边形外角的性质与计算；②涉及核心数学概念包括外角和定理、多边形内角与外角关系；③作图要点：使用 Ray, Rotate, Angle, Point, Line, Circle, Intersect, Segment, Polygon 等GeoGebra命令构建五边形并测量外角；④适合初中及以上学生用于理解多边形几何性质，也可用于动态演示几何变换。

GeoGebra 命令及参数

  1. Ray(A, B) → f
  2. Rotate(A, α, B) → A'
  3. Angle(A, B, A') → β
  4. Ray(B, A') → g
  5. Point(g) → C
  6. Line(C, f) → h
  7. Circle(C, 2) → c
  8. Intersect(c, h) → D, E
  9. Intersect(c, g, 2) → F
  10. Ray(C, A) → i
  11. Angle(B, C, A) → γ
  12. Rotate(B, δ, C) → B'
  13. Angle(B, C, B') → ε
  14. Ray(C, B') → j
  15. Line(A, g) → k
  16. Intersect(k, j) → H
  17. Segment(C, H) → l
  18. Point(l) → G
  19. Line(G, g) → m
  20. Line(B, A) → n
  21. Intersect(m, n) → I
  22. Angle(C, G, I) → ζ
  23. Rotate(C, η, G) → C'
  24. Angle(C, G, C') → θ_1
  25. Ray(G, C') → p
  26. Intersect(n, p) → J
  27. Segment(G, J) → q
  28. Point(q) → K
  29. Ray(K, A) → r
  30. Line(C, G) → s
  31. Line(G, K) → t
  32. Line(K, A) → a
  33. Line(B, C) → b
  34. Segment(B, C) → d
  35. Segment(C, G) → e
  36. Segment(G, K) → f_1
  37. Segment(K, A) → g_1
  38. Segment(A, B) → h_1
  39. Min({d, e, f_1, g_1, h_1}) → o
  40. Circle(B, (0.3 * o)) → c_1
  41. Circle(C, (0.3 * o)) → d_1
  42. Circle(G, (0.3 * o)) → e_1
  43. Circle(K, (0.3 * o)) → k_1
  44. Circle(A, (0.3 * o)) → p_1
  45. Intersect(c_1, n) → L, M
  46. Intersect(c_1, b) → N, O
  47. Intersect(d_1, b) → P, Q
  48. Intersect(d_1, s) → R, S
  49. Intersect(e_1, t) → T, U
  50. Intersect(e_1, s) → V, W
  51. Intersect(k_1, t) → Z, A_1
  52. Intersect(k_1, a) → B_1, C_1
  53. Intersect(p_1, n) → D_1, E_1
  54. Intersect(p_1, a) → F_1, G_1
  55. Line(G, A) → i_1
  56. CircleSector(B, O, L) → q_1
  57. CircleSector(C, S, Q) → r_1
  58. CircleSector(A, D_1, G_1) → c_2
  59. CircleSector(K, C_1, A_1) → t_1
  60. CircleSector(G, U, W) → s_1
  61. Polygon(B, A, K, G, C) → poly1, b_1, a_1, k_2, g_2, c_3
  62. Dilate(A, If[0 < u ≤ 1, 1 - u, 0], B) → A'_1
  63. Vector(A, A'_1) → v
  64. Translate(c_2, v) → d_2
  65. Dilate(B, If[1 < u ≤ 2, 2 - u, 0], C) → B'_1
  66. Vector(B, B'_1) → w
  67. Translate(q_1, w) → e_2
  68. Translate(d_2, w) → f_2
  69. Dilate(C, If[2 < u ≤ 3, 3 - u, 0], G) → C'_1
  70. Vector(C, C'_1) → u_1
  71. Translate(e_2, u_1) → h_2
  72. Translate(f_2, u_1) → p_2
  73. Translate(r_1, u_1) → q_2
  74. Dilate(G, If[3 < u ≤ 4, 4 - u, 0], K) → G'
  75. Vector(G, G') → v_1
  76. Translate(q_2, v_1) → r_2
  77. Translate(s_1, v_1) → s_2
  78. Translate(h_2, v_1) → t_2
  79. Translate(p_2, v_1) → d_3
  80. CircleArc(A, D_1, G_1) → e_3
  81. CircleArc(B, O, L) → f_3
  82. CircleArc(C, S, Q) → g_3
  83. CircleArc(G, U, W) → h_3