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可视化三角形：判断三段能否构成三角形

可视化三角形：判断三段能否构成三角形
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2022-11-09 23:05
测试改名0几何作图滑块动画
本范例通过动态几何演示，帮助学生理解三条线段能否组成三角形。核心数学概念包括三角形三边关系定理，即任意两边之和大于第三边。作图要点涉及使用GeoGebra命令如Shuffle、Element、Sort、Circle等来构造三角形图形。适合6-8年级学生用于几何学习，适用于课堂教学或在线教育平台。

GeoGebra 命令及参数

  1. Shuffle(Sequence[Random[1, 3], i, 1, 100]) → randomOrderList, {3, 3, 1, 1, 3, 1, 1, 3, 3, 2, 2, 3, 3, 3, 3, 3, 3, 1, 2, 3, 2, 1, 1, 1, 2, 3, 3, 3, 3, 3, 2, 3, 1, 1, 1, 3, 1, 3, 3, 1, 1, 1, 3, 1, 3, 2, 3, 1, 2, 3, 2, 3, 2, 3, 1, 3, 2, 3, 3, 2, 3, 3, 1, 2, 3, 3, 2, 1, 1, 3, 2, 3, 3, 3, 1, 3, 1, 2, 3, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 3, 1, 2, 1, 3, 3}
  2. Element(randomOrderList, Mod[countQuestion, 100] + 1) → randomOrder
  3. Shuffle(Sequence[Random[10, 30], i, 1, 100]) → randomSideList2, {17, 15, 30, 20, 12, 20, 24, 16, 23, 29, 25, 23, 12, 23, 19, 14, 11, 30, 25, 15, 13, 27, 22, 20, 28, 17, 11, 20, 17, 30, 20, 30, 23, 28, 23, 14, 20, 21, 24, 16, 16, 20, 25, 12, 16, 10, 30, 26, 18, 14, 25, 10, 17, 18, 22, 24, 27, 19, 13, 27, 19, 10, 25, 20, 22, 19, 11, 21, 15, 12, 28, 30, 21, 17, 17, 19, 20, 25, 17, 21, 13, 10, 22, 30, 28, 22, 14, 30, 28, 19, 24, 16, 26, 27, 20, 13, 22, 12, 26, 26}
  4. Element(randomSideList2, Mod[countQuestion, 100] + 1) → randomSide2
  5. Shuffle(Sequence[Random[20, 50], i, 1, 100]) → randomSideList1, {33, 45, 28, 50, 29, 47, 35, 35, 37, 42, 36, 42, 43, 21, 37, 40, 26, 22, 30, 50, 40, 49, 31, 29, 32, 29, 50, 43, 23, 32, 21, 42, 26, 40, 40, 23, 24, 26, 31, 35, 43, 27, 45, 24, 37, 29, 46, 25, 37, 39, 46, 29, 23, 42, 50, 33, 21, 21, 35, 30, 49, 22, 50, 35, 35, 27, 25, 29, 45, 41, 26, 26, 35, 40, 42, 25, 44, 24, 29, 45, 31, 27, 47, 43, 30, 38, 23, 27, 26, 47, 42, 21, 26, 49, 26, 49, 47, 32, 23, 44}
  6. Element(randomSideList1, Mod[countQuestion, 100] + 1) → randomSide1
  7. Shuffle(Sequence[Random[-10, 5], i, 1, 100]) → randomSideAddendList, {-6, 5, -3, -10, -9, -4, 1, 1, -3, 2, -7, -8, -8, -2, 4, -9, -10, -5, 4, 4, -9, -5, 1, -8, -4, -4, 3, 4, -7, -7, -5, 1, 0, -3, 2, 3, -4, -7, -7, 5, 5, -1, -2, -7, -1, 4, -6, -2, -4, -3, -2, 5, 0, 3, -5, -6, -5, -6, -4, 3, 2, -6, 1, 4, -2, -10, 0, -3, -10, 1, -2, -7, -7, -3, -9, -3, -1, -3, 4, -7, 4, 3, 0, 1, -4, -1, -10, -4, 1, 0, 4, 0, -1, -10, -4, -7, 5, -9, -9, -3}
  8. Sort({randomSide1, randomSide2, randomSide3}) → sideOrder
  9. Element(sideStartPoints, Mod[randomOrder + 1, 3] + 1) → PointSideStart2
  10. Element(sideStartPoints, Mod[randomOrder + 2, 3] + 1) → PointSideStart3
  11. Element(sideStartPoints, Mod[randomOrder, 3] + 1) → PointSideStart1
  12. Circle(PointSideStart1, randomSide1) → sideCircle1
  13. Ray(PointSideStart1, Vector[(1, 0)]) → sideRay1
  14. Segment(PointSideStart1, Intersect[sideCircle1, sideRay1]) → side1
  15. Min({1, ratioHeight, ratioWidth}) → ratioChoice
  16. Distance(PointSideStart2, PointStartAnimationS1_a) → animationRange3
  17. Distance(PointSideStart3, PointStartAnimationS1_a) → animationRange1
  18. Distance(PointSideEnd1, (xAnimationEnd, y(PointStartAnimationS1_a))) → animationRange5
  19. If(animationSlider < animationStart5, 0, animationSlider < animationRange, animationSlider - (animationStart5 + 1), animationRange5) → animationSlider5
  20. PartitionPoint(PointSideStart1 + (sideOrder(2), 0), PointStartAnimationS2_a, animationSlider5, animationRange5) → PointMoveAnimation5
  21. Circle(PointMoveAnimation5, solutionLengths(1)) → circleSolution2
  22. If(animationSlider < animationStart3, 0, animationSlider < animationStart5, animationSlider - (animationStart3 + 1), animationRange3) → animationSlider3
  23. PartitionPoint(PointSideStart2, PointStartAnimationS1_a, animationSlider3, animationRange3) → PointMoveAnimation3
  24. Circle(PointMoveAnimation3, solutionLengths(2)) → circleSolution1
  25. Ray(PointSideStart2, Vector[(1, 0)]) → sideRay2
  26. Circle(PointSideStart2, randomSide2) → sideCircle2
  27. Segment(PointSideStart2, Intersect[sideCircle2, sideRay2]) → side2
  28. PartitionPoint(PointSideStart2 + (sideOrder(1), 0), PointStartAnimationS1_b, animationSlider3, animationRange3) → PointMoveAnimation3b
  29. Ray(PointSideStart3, Vector[(1, 0)]) → sideRay3
  30. Circle(PointSideStart3, randomSide3) → sideCircle3
  31. Segment(PointSideStart3, Intersect[sideCircle3, sideRay3]) → side3
  32. If(sideOrder(1) + sideOrder(2) > sideOrder(3), 1, 2) → correctIndex
  33. Polygon(Zip[PixelsToPoint[Corner[1], Corner[3], Corner[5], A], A, {(pixelsLeft, pixelsTop), (pixelsLeft, y(Corner[5]) - pixelsBottom), Corner[5] - (pixelsRight, pixelsBottom), (x(Corner[5]) - pixelsRight, pixelsTop)}]) → borderBox
  34. Corner(5) → Dims
  35. If(animationSlider < animationRange1, animationSlider, animationRange1) → animationSlider1
  36. PartitionPoint(PointSideStart3, PointStartAnimationS1_a, animationSlider1, animationRange1) → PointMoveAnimation1
  37. If(sideOrder(1) + sideOrder(2) < sideOrder(3), "<", sideOrder(1) + sideOrder(2) > sideOrder(3), ">", "=") → textInequality
  38. If(sideOrder(1) + sideOrder(2) < sideOrder(3), "less than", sideOrder(1) + sideOrder(2) > sideOrder(3), "greater than", "equal to") → textInequalityWord
  39. If(correctIndex ≟ 1, "can", "cannot") → textCanCannot
  40. Point(circleSolution1) → PointMoveAnimation3c_{1}
  41. Polygon({(minXGrid, minYGrid), (minXGrid, maxYGrid), (maxXGrid, maxYGrid), (maxXGrid, minYGrid)}) → solutionGridArea
  42. PartitionPoint(PointSideStart3 + (sideOrder(3), 0), PointStartAnimationS2_a, animationSlider1, animationRange1) → PointMoveAnimation1b
  43. Segment(PointMoveAnimation1, PointMoveAnimation1b) → segmentAnimation1
  44. Segment(PointMoveAnimation3, PointMoveAnimation3b) → segmentAnimation3
  45. PartitionPoint(PointSideStart1, PointStartAnimationS2_b, animationSlider5, animationRange5) → PointMoveAnimation5b
  46. Segment(PointMoveAnimation5, PointMoveAnimation5b) → segmentAnimation5
  47. Point(circleSolution2) → PointMoveAnimation7
  48. Point(circleSolution1) → PointMoveAnimation3c
  49. Segment(PointStartAnimationS1_a, PointMoveAnimation3c) → segmentAnimation6
  50. Point(circleSolution2) → PointMoveAnimation5c
  51. Segment(PointStartAnimationS2_a, PointMoveAnimation5c) → segmentAnimation7
  52. Sequence(PointStarts(n) + (((-Element[textDims2, n, 1])) / 2, (5 * Element[textDims2, n, 2] / 4)) - (Element[textDims2, n, 3], Element[textDims2, n, 4]), n, 1, 3) → PointTextStarts
  53. PointToPixels(Corner[1], Corner[3], Corner[5], PointMoveAnimation5c) → OnboardingPoint
  54. onboardingTextOffset(Corner[onboardingText, 1], Corner[onboardingText, 3], onboardingCase, Corner[1], Corner[3], Corner[5]) → OnboardingTextOffset
  55. circlePixels(PointMoveAnimation5c, 7 + (7 * pulsing), Corner[1], Corner[3], Corner[5]) → pulsingObject

AI 绘图提示语参考

在平面直角坐标系中，给定三条线段长度参数，并从同一点出发构造三段依次相接的边，形成一个三角形的三条边。使用两侧的圆与射线来确定每条边的端点：先在第一条边的起点作以其长度为半径的圆，并取与水平射线的交点得到第一条边；再在第二条边的起点作对应半径的圆取与水平射线的交点得到第二条边；第三条边以其半径圆与水平射线交点确定端点。最后把三段首尾连接成封闭的三角形轮廓，并给出相应的三边关系文字提示（用“<、>、=”与“可以/不可以”表述），强调两边之和与第三边的大小比较。
以上提示语为根据原始绘图命令整理而来，仅供参考。