积极 AI Logo 积极 AI

平行四边形对角线性质演示

平行四边形对角线性质演示
几何画板及绘图内容加载中，请稍等……
2019-05-29 20:46
向量几何作图
①本范例演示平行四边形对角线的交点性质及分割关系；②涉及核心数学概念包括平行四边形、对角线、中点、角平分线、向量等；③构造要点运用了Polygon, PointIn, Intersect, Mirror, Circle, Line, Segment, Midpoint, Angle, AreParallel等GeoGebra命令与对象；④适合初中及以上数学教学，用于直观理解平行四边形几何性质。

GeoGebra 命令及参数

  1. Polygon({(-6, 19), (26, 19), (26, 0), (-6, 0)}) → viewBox
  2. PointIn(viewBox) → paraA
  3. PointIn(viewBox) → paraB
  4. PointIn(viewBox) → recB
  5. PointIn(viewBox) → sqB
  6. PointIn(viewBox) → rhomB
  7. PointIn(viewBox) → recA
  8. Point(OrthogonalLine[recB, Line[recA, recB]]) → recC
  9. Intersect(Line[recA, Line[recB, recC]], Line[recC, Line[recA, recB]]) → recD
  10. PointIn(viewBox) → sqA
  11. Mirror(sqA, AngularBisector[Line[sqA, sqB], OrthogonalLine[sqB, Line[sqA, sqB]]]) → sqC
  12. Intersect(Line[sqA, Line[sqB, sqC]], Line[sqC, Line[sqA, sqB]]) → sqD
  13. PointIn(viewBox) → rhomA
  14. Circle(rhomB, rhomA) → circle1forRhombus
  15. Point(circle1forRhombus) → rhomC
  16. Mirror(rhomB, Line[rhomA, rhomC]) → rhomD
  17. PointIn(viewBox) → paraC
  18. If(showParallelogram, paraC, If[showRectangle, recC, If[showRhombus, rhomC, sqC]]) → C
  19. If(showParallelogram, paraB, If[showRectangle, recB, If[showRhombus, rhomB, sqB]]) → B
  20. Line(B, C) → lineRight
  21. If(showParallelogram, paraA, If[showRectangle, recA, If[showRhombus, rhomA, sqA]]) → A
  22. Line(A, B) → lineTop
  23. Intersect(Line[paraA, lineRight], Line[paraC, lineTop]) → paraD
  24. Segment(A, C) → AC
  25. Polygon({(-11.5, 9), (-9, 7.5), (-11.5, 6), (-14, 7.5)}) → selectorShapeRhombus
  26. Polygon({(-19, 10), (-8, 11), (-8, 5), (-19, 4)}) → selectorShapeParallelogram
  27. LaTeX((((("\text{" * QUESTION) * "\\") * INSTRUCTIONS) * "}")) → TEXT
  28. Polygon({(-19.5, 19.5), (-7.5, 19.5), (-7.5, 3.5), (-19.5, 3.5)}) → selectorBoxQuadrilateral
  29. Polygon({(-12, 8), (-12, 7), (-11, 7), (-11, 8)}) → selectorShapeSquare2
  30. Polygon({Vertex[selectorShapeRhombus]}) → selectorBorderRhombus
  31. Polygon({Vertex[selectorShapeParallelogram]}) → selectorBorderParallelogram
  32. Polygon({Vertex[selectorShapeSquare2]}) → selectorBorderSquare2
  33. If(showParallelogram, paraD, If[showRectangle, recD, If[showRhombus, rhomD, sqD]]) → D
  34. Segment(A, B) → AB
  35. Segment(A, D) → AD
  36. Segment(B, C) → BC
  37. Segment(D, B) → DB
  38. Segment(D, C) → DC
  39. Midpoint(AB) → midAB
  40. Midpoint(AD) → midAD
  41. Midpoint(BC) → midBC
  42. Midpoint(D, C) → midDC
  43. Segment(A, Midpoint[Segment[midAB, B]]) → AB_1
  44. Segment(Midpoint[Segment[midAB, A]], B) → AB_2
  45. Segment(Midpoint[Segment[midAD, D]], A) → AD_1
  46. Segment(Midpoint[Segment[midAD, A]], D) → AD_2
  47. Segment(Midpoint[Segment[midBC, C]], B) → BC_1
  48. Segment(Midpoint[Segment[midBC, B]], C) → BC_2
  49. Segment(D, Midpoint[Segment[midDC, C]]) → DC_1
  50. Segment(Midpoint[Segment[midDC, D]], C) → DC_2
  51. Polygon({A, B, C, D}) → quadrilateral
  52. Intersect(AC, DB) → E
  53. Angle(A, B, C) → ABC
  54. Angle(B, C, D) → BCD
  55. Angle(C, D, A) → CDA
  56. Angle(D, A, B) → DAB
  57. Line(A, D) → lineLeft
  58. Line(D, C) → lineBottom
  59. AreParallel(lineLeft, lineRight) → parallelLeftRight
  60. AreParallel(lineTop, lineBottom) → parallelTopBottom
  61. LaTeX(UnicodeToLetter[10003]) → cmark
  62. LaTeX(UnicodeToLetter[10007]) → xmark
  63. LaTeX(Distance[A, E]) → labelAE
  64. LaTeX(Distance[B, E]) → labelBE
  65. LaTeX(Distance[C, E]) → labelCE
  66. LaTeX(Distance[D, E]) → labelDE
  67. Angle(A, E, D) → AED
  68. Polygon({(-18, 5), (-18, 9.5), (-15, 9.5), (-15, 5)}) → selectorShapeRectangle
  69. Polygon({Vertex[selectorShapeRectangle]}) → selectorBorderRectangle
  70. Polygon({(-17, 7), (-17, 8), (-16, 8), (-16, 7)}) → selectorShapeSquare1
  71. Polygon({Vertex[selectorShapeSquare1]}) → selectorBorderSquare1

AI 绘图提示语参考

绘制一个平行四边形，然后画出其对角线并找到交点。接着画一个矩形和一个菱形，分别找到它们的对角线交点。最后，画出每个图形的对角线，并标出每个对角线的中点。
以上提示语为根据原始绘图命令整理而来，仅供参考。