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无言证明：平行四边形性质

无言证明：平行四边形性质
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2016-01-14 17:44
多边形向量几何作图
此范例通过拖动点和滑块，展示了平行四边形的性质。它证明了平行四边形对角线互相平分。通过构造平行四边形的对角线，利用点、线段、向量、平移等GeoGebra命令，直观地展示了这一几何性质。适合初中及以上学生学习几何变换与证明。

GeoGebra 命令及参数

  1. Point(xAxis) → A
  2. Intersect(xAxis, yAxis) → B
  3. CircleArc(B, D, A) → c
  4. Point(c) → E
  5. Segment(A, E) → a
  6. Segment(E, F) → b
  7. Segment(C, E) → d
  8. Segment(E, G) → e
  9. Line(F, a) → f
  10. Line(G, d) → g
  11. Intersect(f, g) → H
  12. Segment(A, C) → h
  13. Line(H, E) → i
  14. Intersect(i, h) → I
  15. Line(A, i) → j
  16. Line(C, i) → k
  17. Vector(H, E) → u
  18. Translate(I, u) → I'
  19. Line(I', h) → l
  20. Intersect(j, l) → J
  21. Intersect(k, l) → K
  22. Vector(E, A) → v
  23. Vector(E, C) → w
  24. Translate(G, w) → G'
  25. Translate(F, v) → F'
  26. Polygon(A, E, F, F') → poly1, a_1, e_1, f_1, f'
  27. Polygon(A, J, K, C) → poly2, a_2, j_1, k_1, c_1
  28. Polygon(E, G, G', C) → poly3, e_2, g_1, g', c_2
  29. Dilate(F, If[m < 1, 1 - m, 0], H) → F'_1
  30. Dilate(G, If[m < 1, 1 - m, 0], H) → G'_1
  31. Translate(F'_1, v) → L
  32. Translate(G'_1, w) → M
  33. Polygon(A, L, F'_1, E) → poly4, a_3, l_1, f'_1, e_3
  34. Polygon(E, G'_1, M, C) → poly5, e_4, g'_1, m_1, c_3
  35. Vector(E, I) → n
  36. Translate(H, n) → H'
  37. Dilate(H, If[1 ≤ m < 2, 2 - m, 0], H') → H'_1
  38. Vector(L, A) → p
  39. Translate(H'_1, p) → N
  40. Polygon(L, H'_1, N, A) → poly6, l_2, h'_1, n_1, a_4
  41. Polygon(H'_1, M, C, N) → poly7, h'_2, m_2, c_4, n_2
  42. Dilate(I, If[2 ≤ m < 3, 3 - m, 0], I') → I'_1
  43. Vector(A, L) → q
  44. Translate(I'_1, q) → O
  45. Vector(I, A) → r
  46. Translate(O, r) → O'
  47. Translate(I'_1, r) → P
  48. Vector(I, C) → s
  49. Translate(O, s) → O'_1
  50. Translate(I'_1, s) → Q
  51. Polygon(O, O', P, I'_1) → poly8, o, o', p_1, i'_1
  52. Polygon(O, O'_1, Q, I'_1) → poly9, o_1, o'_1, q_1, i'_2