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无言证明 by Steve Phelps

无言证明 by Steve Phelps
几何画板及绘图内容加载中，请稍等……
2015-02-03 06:21
测试改名0向量几何作图
拖动点A和B，观察图形的变化。这个范例通过动态几何展示了三角形的中线定理。它利用了点、交点、镜像、圆弧、线段、多边形、射线、重心、向量、平移等GeoGebra命令。适合初中及以上学生学习几何证明。

GeoGebra 命令及参数

  1. Point(xAxis) → A
  2. Intersect(xAxis, yAxis) → B
  3. Mirror(A, B) → A'
  4. CircleArc(B, C, A) → c
  5. Point(c) → D
  6. Segment(A, D) → a
  7. Segment(D, A') → b
  8. Segment(A', A) → d
  9. Polygon(D, A', 4) → poly1, e, f, g, p, E, H
  10. Ray(E, H) → s
  11. Polygon(A, D, 4) → poly3, k, l, m, q, G, J
  12. Ray(J, G) → r
  13. Ray(E, H) → t
  14. Intersect(r, t) → K
  15. Polygon(D, G, K) → poly4, k_1, d_1, g_1
  16. Polygon(D, H, K) → poly5, k_2, d_2, h_1
  17. Polygon(A, D, A') → poly6, a', a_1, d_3
  18. Centroid(poly4) → F
  19. Centroid(poly5) → I
  20. Centroid(poly6) → L
  21. Vector(G, J) → u
  22. Vector(H, E) → v
  23. Translate(F, u) → F'
  24. Translate(I, v) → I'
  25. Segment(F, F') → h
  26. Segment(I, I') → i
  27. Point(h) → M
  28. Vector(F, M) → w
  29. Point(i) → N
  30. Vector(I, N) → j
  31. Translate(D, j) → D'
  32. Translate(H, j) → H'
  33. Translate(K, j) → K'
  34. Polygon(D', H', K') → poly5', k', d', h'
  35. Translate(D, w) → D'_1
  36. Translate(G, w) → G'
  37. Translate(K, w) → K'_1
  38. Polygon(D'_1, G', K'_1) → poly4', k'_1, d'_1, g'
  39. Vector(D, K) → n
  40. Translate(L, n) → L'
  41. Segment(L, L') → b_1
  42. Point(b_1) → O
  43. Vector(L, O) → u_1
  44. Translate(A, u_1) → A'_1
  45. Translate(D, u_1) → D'_2
  46. Translate(A', u_1) → A''
  47. Polygon(A'_1, D'_2, A'') → poly6', a'', a'_1, d'_2
  48. Segment(A, A') → c_1
  49. Segment(E, K) → e_1
  50. Segment(G, K) → f_1