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正交中心与菱形演示

正交中心与菱形演示
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2015-10-22 09:46
测试改名0最值优化几何作图
①本范例演示了正交中心在三角形中的位置及其与菱形的关系；②涉及核心数学概念包括正交中心、菱形性质、向量运算、几何作图；③构造要点：使用Polygon、Midpoint、Segment、Intersect、OrthogonalLine、Distance、Angle等命令绘制三角形、菱形，并计算正交中心；④适合高中数学教学，用于理解三角形几何性质和优化问题。

GeoGebra 命令及参数

  1. Polygon(A, B, C) → poly1, c, a, b
  2. Midpoint(c) → D
  3. Midpoint(a) → E
  4. Midpoint(b) → F
  5. Segment(A, E) → d
  6. Segment(C, D) → e
  7. Segment(B, F) → f
  8. Intersect(d, e) → Centroid
  9. Polygon(A_1, B_1, C_1) → poly1_1, c_1, a_1, b_1
  10. Midpoint(c_1) → D_1
  11. Midpoint(a_1) → E_1
  12. Midpoint(b_1) → F_1
  13. OrthogonalLine(C_1, c_1) → g
  14. OrthogonalLine(A_1, a_1) → h
  15. OrthogonalLine(B_1, b_1) → i
  16. Intersect(g, h) → Orthocenter
  17. Distance(A, F) → distanceAF
  18. Midpoint(A, F) →
  19. Distance(F, C) → distanceFC
  20. Midpoint(F, C) →
  21. Distance(A, D) → distanceAD
  22. Midpoint(A, D) →
  23. Distance(D, B) → distanceDB
  24. Midpoint(D, B) →
  25. Distance(B, E) → distanceBE
  26. Midpoint(B, E) →
  27. Distance(E, C) → distanceEC
  28. Midpoint(E, C) →
  29. Distance(B, F) → distanceBF
  30. Midpoint(B, F) →
  31. Distance(A, E) → distanceAE
  32. Midpoint(A, E) →
  33. Distance(C, D) → distanceCD
  34. Midpoint(C, D) →
  35. Angle(A_1, B_1, C_1) → δ
  36. Angle(B_1, C_1, A_1) → ε
  37. Angle(C_1, A_1, B_1) → ζ
  38. Intersect(g, c_1) → G
  39. Intersect(h, a_1) → H
  40. Intersect(i, b_1) → I
  41. Angle(Orthocenter, G, B_1) → α
  42. Angle(Orthocenter, H, C_1) → β
  43. Angle(C_1, I, Orthocenter) → γ