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风筝形对角线性质探究（LR7-03-XT3）

风筝形对角线性质探究（LR7-03-XT3）
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2019-05-31 03:46
多边形角变换几何作图滑块动画
①本范例通过GeoGebra动态演示风筝形（kite）对角线的性质，包括对角线互相垂直以及其中一条对角线被另一条平分等几何关系。②核心数学概念涉及四边形分类、风筝形的定义、对角线性质、对称性以及几何构造中的交点、中点、垂直关系。③作图要点：从构造摘要可见，使用了Polygon、PointIn、Mirror、Circle、Point、Intersect、If、Segment、LaTeX、Midpoint、Angle、Line、AreParallel等命令，构建了风筝形及其辅助圆、菱形、正方形等对象，并通过选择器（selector）切换不同四边形形状，动态展示对角线关系。④适合中学几何教学，尤其适用于八年级或九年级学习四边形性质、几何证明及动态探究场景，也可用于教师课堂演示或学生自主探索。

GeoGebra 命令及参数

  1. Polygon({(-6, 19), (26, 19), (26, 0), (-6, 0)}) → viewBox
  2. PointIn(viewBox) → sqA
  3. PointIn(viewBox) → sqB
  4. Mirror(sqA, AngularBisector[Line[sqA, sqB], OrthogonalLine[sqB, Line[sqA, sqB]]]) → sqC
  5. PointIn(viewBox) → kiteA
  6. PointIn(viewBox) → kiteC
  7. PointIn(viewBox) → rhomB
  8. PointIn(viewBox) → rhomA
  9. Circle(rhomB, rhomA) → circle1forRhombus
  10. Point(circle1forRhombus) → rhomC
  11. Mirror(rhomB, Line[rhomA, rhomC]) → rhomD
  12. Intersect(Line[sqA, Line[sqB, sqC]], Line[sqC, Line[sqA, sqB]]) → sqD
  13. If(showKite, kiteC, If[showRhombus, rhomC, sqC]) → C
  14. If(showKite, kiteA, If[showRhombus, rhomA, sqA]) → A
  15. Segment(A, C) → AC
  16. Circle(Midpoint[AC], kiteA) → circle1forKite
  17. PointIn(circle1forKite) → kiteB
  18. Polygon({(-11.5, 9), (-9, 7.5), (-11.5, 6), (-14, 7.5)}) → selectorShapeRhombus
  19. Mirror(kiteB, Line[kiteA, kiteC]) → kiteD
  20. LaTeX((((("\text{" * QUESTION) * "\\") * INSTRUCTIONS) * "}")) → TEXT
  21. Polygon({(-8, 7.5), (-11.5, 11), (-19, 7.5), (-11.5, 4)}) → selectorShapeKite
  22. Polygon({(-19.5, 19.5), (-7.5, 19.5), (-7.5, 3.5), (-19.5, 3.5)}) → selectorBoxQuadrilateral
  23. Polygon({(-12, 8), (-12, 7), (-11, 7), (-11, 8)}) → selectorShapeSquare
  24. Polygon({Vertex[selectorShapeRhombus]}) → selectorBorderRhombus
  25. Polygon({Vertex[selectorShapeKite]}) → selectorBorderKite
  26. Polygon({Vertex[selectorShapeSquare]}) → selectorBorderSquare
  27. If(showKite, kiteD, If[showRhombus, rhomD, sqD]) → D
  28. If(showKite, kiteB, If[showRhombus, rhomB, sqB]) → B
  29. Segment(A, B) → AB
  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, B) → lineTop
  53. Line(A, D) → lineLeft
  54. Line(D, C) → lineBottom
  55. Line(B, C) → lineRight
  56. AreParallel(lineLeft, lineRight) → parallelLeftRight
  57. AreParallel(lineTop, lineBottom) → parallelTopBottom
  58. LaTeX(UnicodeToLetter[10003]) → cmark
  59. LaTeX(UnicodeToLetter[10007]) → xmark
  60. LaTeX(Distance[A, E]) → labelAE
  61. LaTeX(Distance[B, E]) → labelBE
  62. LaTeX(Distance[C, E]) → labelCE
  63. LaTeX(Distance[D, E]) → labelDE
  64. Angle(A, E, D) → AED