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梯形中位线探究

梯形中位线探究
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2019-01-24 10:06
多边形三角函数解析几何几何作图滑块动画
①本范例动态演示梯形中位线的性质与定理；②涉及核心数学概念：梯形、中位线、平行线、几何变换；③作图要点：使用Line, Ray, Point, Segment, Slope, Midpoint, Vector, Translate, Rotate等GeoGebra命令构建图形并展示中位线与底边平行且等于两底和的一半；④适合初中及以上数学教学，用于直观理解几何定理。

GeoGebra 命令及参数

  1. Line(A, B) → f
  2. Ray(A, B) → g
  3. Point(g) → C
  4. Ray(A, C) → h
  5. Segment(A, C) → i
  6. Slope(f) → m
  7. PointIn(a) → D
  8. Segment(A, D) → j
  9. Line(D, i) → k
  10. Point(k) → E
  11. Ray(D, E) → l
  12. Point(l) → F
  13. Ray(D, F) → n
  14. Segment(F, C) → p
  15. Segment(D, F) → q
  16. Min(j, i) → c
  17. Circle(A, (0.2 * c)) → d
  18. Intersect(d, j, 1) → G
  19. Intersect(d, i, 1) → H
  20. CircleSector(A, H, G) → e
  21. Angle(C, A, D) → α
  22. CircleSector(A, G, H) → r
  23. Dilate(A, If[0 < o ≤ 1, 1 - o, 0], C) → A'
  24. Midpoint(D, A) → I
  25. Midpoint(F, C) → J
  26. Segment(A, A') → s
  27. Dilate(F, If[0 < o ≤ 1, 1 - o, 0], D) → F'
  28. Segment(F, F') → t
  29. Dilate(A, If[1 < o ≤ 2, 2 - o, 0], D) → A'_1
  30. Segment(A, A'_1) → f_1
  31. Ray(A, D) → g_1
  32. Point(g_1) → K
  33. Ray(D, K) → h_1
  34. Dilate(A, If[2 < o ≤ 3, 3 - o, 0], D) → A'_2
  35. Vector(A, A'_2) → u
  36. Translate(e, u) → e'
  37. Dilate(A, If[3 < o ≤ 4, 4 - o, 0], I) → A'_3
  38. Dilate(C, If[3 < o ≤ 4, 4 - o, 0], J) → C'
  39. Segment(A, A'_3) → i_1
  40. Segment(C, C') → j_1
  41. Dilate(I, If[4 < o ≤ 5, 5 - o, 0], D) → I'
  42. Dilate(J, If[4 < o ≤ 5, 5 - o, 0], F) → J'
  43. Segment(I, I') → k_1
  44. Segment(J, J') → l_1
  45. Rotate(A, If[5 < o ≤ 6, ((o - 5) * π), π], I) → A'_4
  46. Rotate(A'_3, If[5 < o ≤ 6, ((o - 5) * π), π], I) → L
  47. Segment(A'_4, L) → m_1
  48. Polygon(A, C, F, D) → poly1, a_1, c_1, f_2, d_1
  49. Rotate(C, If[5 < o ≤ 6, ((-(o - 5)) * π), (-π)], J) → C'_1
  50. Rotate(C', If[5 < o ≤ 6, ((-(o - 5)) * π), (-π)], J) → C''
  51. Segment(C'_1, C'') → n_1
  52. Dilate(I, If[6 < o ≤ 7, 7 - o, 0], J) → I'_1
  53. Segment(I, I'_1) → p_1
  54. Dilate(D, If[7 < o ≤ 8, 8 - o, 0], I) → D'
  55. Vector(D, D') → v
  56. Translate(e', v) → e''
  57. Translate(r, u) → r'
  58. Translate(r', v) → r''
  59. Rotate(A, If[8.5 < o ≤ 9.5, ((-(o - 8.5)) * π), (-π)], J) → A'_5
  60. Rotate(C, If[8.5 < o ≤ 9.5, ((-(o - 8.5)) * π), (-π)], J) → C'_2
  61. Rotate(F, If[8.5 < o ≤ 9.5, ((-(o - 8.5)) * π), (-π)], J) → F'_1
  62. Rotate(D, If[8.5 < o ≤ 9.5, ((-(o - 8.5)) * π), (-π)], J) → D'_1
  63. Polygon(A'_5, C'_2, F'_1, D'_1) → poly1', a'_5, c'_2, f'_1, d'_1
  64. Dilate(I, If[10 < o ≤ 11, 11 - o, 0], D) → I'_2
  65. Vector(I, I'_2) → w
  66. Translate(I, w) → I'_3
  67. Translate(I'_1, w) → M
  68. Segment(I'_3, M) → q_1
  69. Dilate(I, If[11 < o ≤ 12, 12 - o, 0], M) → I'_4
  70. Dilate(I, If[11 < o ≤ 12, 12 - o, 0], M) → I'_5
  71. Vector(I, I'_5) → u_1
  72. Translate(I, u_1) → I'_6
  73. Translate(I'_1, u_1) → N
  74. Segment(I'_6, N) → r_1