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三角形中线定理动态演示

三角形中线定理动态演示
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2016-06-18 04:12
测试改名0向量几何作图
所属专题 Congruence (CO) Cluster Congruence (Vol 2) CCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 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 CCSS High School: Geometry (Congruence) Volume 2 Triangle Theorems
该范例通过动态图形展示了三角形中线定理，无需文字和数字说明。它包括定义提示和引导性证明问题。使用了Segment, Line, Slope, PointIn, Min, Midpoint, Circle, Intersect, Angle, Rotate, Polygon, Dilate, Vector, CircleSector, Translate等GeoGebra命令。适合初中及以上学生学习几何作图。

GeoGebra 命令及参数

  1. Segment(A, B) → g
  2. Line(A, B) → f
  3. Slope(f) → m
  4. PointIn(a) → C
  5. Segment(C, A) → i
  6. Segment(B, C) → h
  7. Min(list1) → d
  8. Midpoint(C, A) → F
  9. Circle(F, (0.15 * d)) → e_1
  10. Midpoint(B, C) → E
  11. Line(F, E) → i_1
  12. Intersect(e_1, i_1) → O, P
  13. Angle(P, F, C) → β
  14. Rotate(P, If[9 < l ≤ 10, ((l - 9) * β), β], F) → P'_2
  15. Polygon(A, B, C) → poly1, c, a_1, b_1
  16. Midpoint(A, B) → D
  17. Circle(F, (0.15 * d)) → e
  18. Segment(F, E) → j
  19. Intersect(e, i) → G, H
  20. Intersect(e, j, 1) → I
  21. Dilate(A, If[0 < l ≤ 1, 1 - l, 0], D) → A'
  22. Segment(A, A') → n
  23. Dilate(D, If[1 < l ≤ 2, 2 - l, 0], B) → D'
  24. Segment(D, D') → p
  25. Rotate(A, If[2 < l ≤ 3, ((-(l - 2)) * π), (-π)], D) → A'_1
  26. Rotate(A', If[2 < l ≤ 3, ((l - 2) * π), π], D) → A''
  27. Segment(A'_1, A'') → n'
  28. Dilate(B, If[3 < l ≤ 4, 4 - l, 0], E) → B'
  29. Segment(B, B') → q
  30. Dilate(E, If[4 < l ≤ 5, 5 - l, 0], C) → E'
  31. Segment(E, E') → r
  32. Rotate(B, If[5 < l ≤ 6, ((-(l - 5)) * π), (-π)], E) → B'_1
  33. Rotate(B', If[5 < l ≤ 6, ((l - 5) * π), π], E) → B''
  34. Segment(B'_1, B'') → q'
  35. Dilate(C, If[6 < l ≤ 7, 7 - l, 0], F) → C'
  36. Segment(C, C') → s
  37. Dilate(F, If[7 < l ≤ 8, 8 - l, 0], A) → F'
  38. Segment(F, F') → t
  39. Rotate(C, If[8 < l ≤ 9, ((-(l - 8)) * π), (-π)], F) → C'_1
  40. Rotate(C', If[8 < l ≤ 9, ((l - 8) * π), π], F) → C''
  41. Segment(C'_1, C'') → s'
  42. Dilate(F, If[9 < l ≤ 10, 10 - l, 0], E) → F'_1
  43. Segment(F, F'_1) → f_1
  44. Dilate(F, If[10 < l ≤ 11, 11 - l, 0], A) → F'_2
  45. Vector(F, F'_2) → u
  46. CircleSector(F, P, P'_2) → k
  47. Translate(k, u) → k'
  48. Dilate(E, If[11 < l ≤ 12, 12 - l, 0], D) → E'_1
  49. Vector(E, E'_1) → v
  50. Translate(F, v) → F'_3
  51. Translate(F'_1, v) → J
  52. Segment(F'_3, J) → g_1
  53. Dilate(F, If[12 < l ≤ 13, 13 - l, 0], D) → F'_4
  54. Vector(F, F'_4) → w
  55. Translate(F, w) → F'_5
  56. Translate(F'_1, w) → K
  57. Segment(F'_5, K) → h_1
  58. Angle(C, B, A) → α
  59. Intersect(e, j) → L,
  60. Intersect(e, i, 1) → M
  61. Intersect(i, j) → N
  62. CircleSector(N, M, L) → c_1
  63. Translate(c_1, u) → d_1
  64. Rotate(P, If[9 < l ≤ 10, l - 9]) → P'
  65. Rotate(P, If[9 < l ≤ 10, ((l - 9) * β), β]) → P'_1

AI 绘图提示语参考

绘制一个动态演示三角形中位线定理的几何图形。先画一个任意三角形，标出三边中点，连接其中两个中点形成中位线。用虚线或辅助线展示三角形各边上的动态伸缩过程，例如顶点沿边滑动、边被平移或旋转，以逐步揭示中位线与第三边平行且长度为其一半的关系。图形中可包含小圆点标记中点，以及用扇形或箭头表示旋转或平移方向。整体无文字数字，仅通过视觉动态呈现定理。
以上提示语为根据原始绘图命令整理而来，仅供参考。