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梯形的对角线

梯形的对角线
几何画板及绘图内容加载中，请稍等……
2019-05-28 23:36
多边形角几何作图
这个范例演示梯形的对角线性质。核心数学概念包括梯形的定义、面积计算和对角线的性质。通过使用GeoGebra命令如Polygon、PointIn、Intersect等，可以构造梯形并观察其对角线的交点。适合初中和高中学生学习几何作图和相关性质。

GeoGebra 命令及参数

  1. Polygon({(-6, 19), (26, 19), (26, 0), (-6, 0)}) → viewBox
  2. PointIn(viewBox) → recB
  3. PointIn(viewBox) → paraB
  4. PointIn(viewBox) → trapB
  5. PointIn(viewBox) → recA
  6. PointIn(viewBox) → paraA
  7. PointIn(viewBox) → trapA
  8. PointIn(viewBox) → trapC
  9. Point(Ray[trapC, Vector[trapB, trapA]]) → trapD
  10. PointIn(viewBox) → paraC
  11. If(showTrapezoid, trapB, If[showParallelogram, paraB, recB]) → B
  12. If(showTrapezoid, trapA, If[showParallelogram, paraA, recA]) → A
  13. Line(A, B) → lineTop
  14. Point(OrthogonalLine[recB, lineTop]) → recC
  15. If(showTrapezoid, trapC, If[showParallelogram, paraC, recC]) → C
  16. Line(B, C) → lineRight
  17. Intersect(Line[recA, lineRight], Line[recC, lineTop]) → recD
  18. Intersect(Line[paraA, lineRight], Line[paraC, lineTop]) → paraD
  19. LaTeX((((("\text{" * QUESTION) * "\\") * INSTRUCTIONS) * "}")) → TEXT
  20. Polygon({(-19.5, 19.5), (-7.5, 19.5), (-7.5, 3.5), (-19.5, 3.5)}) → selectorBoxQuadrilateral
  21. Polygon({(-18, 11), (-9, 11), (-8, 4), (-19, 4)}) → selectorShapeTrapezoid
  22. Polygon({(-17, 9), (-10, 10), (-10, 6), (-17, 5)}) → selectorShapeParallelogram
  23. Polygon({(-16, 8), (-16, 7), (-11, 7), (-11, 8)}) → selectorShapeRectangle
  24. Polygon({Vertex[selectorShapeParallelogram]}) → selectorBorderParallelogram
  25. Polygon({Vertex[selectorShapeTrapezoid]}) → selectorBorderTrapezoid
  26. If(showTrapezoid, trapD, If[showParallelogram, paraD, recD]) → D
  27. Polygon({Vertex[selectorShapeRectangle]}) → selectorBorderRectangle
  28. Segment(A, B) → AB
  29. Segment(A, C) → AC
  30. Segment(A, D) → AD
  31. Segment(B, C) → BC
  32. Segment(D, B) → DB
  33. Segment(D, C) → DC
  34. Midpoint(AB) → midAB
  35. Midpoint(AD) → midAD
  36. Midpoint(BC) → midBC
  37. Midpoint(D, C) → midDC
  38. Segment(A, Midpoint[Segment[midAB, B]]) → AB_1
  39. Segment(Midpoint[Segment[midAB, A]], B) → AB_2
  40. Segment(Midpoint[Segment[midAD, D]], A) → AD_1
  41. Segment(Midpoint[Segment[midAD, A]], D) → AD_2
  42. Segment(Midpoint[Segment[midBC, C]], B) → BC_1
  43. Segment(Midpoint[Segment[midBC, B]], C) → BC_2
  44. Segment(D, Midpoint[Segment[midDC, C]]) → DC_1
  45. Segment(Midpoint[Segment[midDC, D]], C) → DC_2
  46. Polygon({A, B, C, D}) → quadrilateral
  47. Intersect(AC, DB) → E
  48. Angle(A, B, C) → ABC
  49. Angle(B, C, D) → BCD
  50. Angle(C, D, A) → CDA
  51. Angle(D, A, B) → DAB
  52. Line(A, D) → lineLeft
  53. Line(D, C) → lineBottom
  54. AreParallel(lineLeft, lineRight) → parallelLeftRight
  55. AreParallel(lineTop, lineBottom) → parallelTopBottom
  56. LaTeX(UnicodeToLetter[10003]) → cmark
  57. LaTeX(UnicodeToLetter[10007]) → xmark
  58. LaTeX(Distance[A, E]) → labelAE
  59. LaTeX(Distance[B, E]) → labelBE
  60. LaTeX(Distance[C, E]) → labelCE
  61. LaTeX(Distance[D, E]) → labelDE

AI 绘图提示语参考

绘制一个梯形，包含四个顶点A、B、C、D。首先绘制一个平行四边形，然后在平行四边形内随机选取四个点作为梯形的顶点。接着画出梯形的两条对角线，观察它们的交点E。最后，画出梯形的两条中位线，即连接每条边的中点。
以上提示语为根据原始绘图命令整理而来，仅供参考。