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按角度分类三角形

按角度分类三角形
几何画板及绘图内容加载中，请稍等……
2018-03-20 23:16
测试改名0角几何作图滑块动画函数图像
①本范例演示如何根据角度大小对三角形进行分类；②涉及核心数学概念包括角度分类（锐角、直角、钝角三角形）、几何作图、条件判断；③构造要点：使用Polygon、If、Min、Max、Element、Point、Circle、Segment、Intersect、Mod、Div、Midpoint、Text、Angle等GeoGebra命令和对象实现动态三角形绘制与分类标注；④适合高中数学教学，用于直观理解三角形分类标准及动态几何演示。

GeoGebra 命令及参数

  1. Polygon((-3.7, -5), (-2.8, -5), 4) → poly9
  2. Polygon((-4.7, -5), (-3.8, -5), 4) → poly8
  3. Polygon((-3.7, -3.5), (-2.8, -3.5), 4) → poly6
  4. Polygon((-4.7, -3.5), (-3.8, -3.5), 4) → poly5
  5. Polygon((-3.7, -2), (-2.8, -2), 4) → poly3
  6. Polygon((-4.7, -2), (-3.8, -2), 4) → poly2
  7. If(IsInRegion[A, poly9], 1, If[IsInRegion[B, poly9], 2, If[IsInRegion[C, poly9], 3, If[IsInRegion[D, poly9], 4, If[IsInRegion[E, poly9], 5, If[IsInRegion[F, poly9], 6, If[IsInRegion[G, poly9], 7, If[IsInRegion[H, poly9], 8, If[IsInRegion[I, poly9], 9, 0]]]]]]]]) → nineSum
  8. If(IsInRegion[A, poly8], 1, If[IsInRegion[B, poly8], 2, If[IsInRegion[C, poly8], 3, If[IsInRegion[D, poly8], 4, If[IsInRegion[E, poly8], 5, If[IsInRegion[F, poly8], 6, If[IsInRegion[G, poly8], 7, If[IsInRegion[H, poly8], 8, If[IsInRegion[I, poly8], 9, 0]]]]]]]]) → eightSum
  9. If(IsInRegion[A, poly6], 1, If[IsInRegion[B, poly6], 2, If[IsInRegion[C, poly6], 3, If[IsInRegion[D, poly6], 4, If[IsInRegion[E, poly6], 5, If[IsInRegion[F, poly6], 6, If[IsInRegion[G, poly6], 7, If[IsInRegion[H, poly6], 8, If[IsInRegion[I, poly6], 9, 0]]]]]]]]) → sixSum
  10. If(IsInRegion[A, poly5], 1, If[IsInRegion[B, poly5], 2, If[IsInRegion[C, poly5], 3, If[IsInRegion[D, poly5], 4, If[IsInRegion[E, poly5], 5, If[IsInRegion[F, poly5], 6, If[IsInRegion[G, poly5], 7, If[IsInRegion[H, poly5], 8, If[IsInRegion[I, poly5], 9, 0]]]]]]]]) → fiveSum
  11. If(IsInRegion[A, poly2], 1, If[IsInRegion[B, poly2], 2, If[IsInRegion[C, poly2], 3, If[IsInRegion[D, poly2], 4, If[IsInRegion[E, poly2], 5, If[IsInRegion[F, poly2], 6, If[IsInRegion[G, poly2], 7, If[IsInRegion[H, poly2], 8, If[IsInRegion[I, poly2], 9, 0]]]]]]]]) → twoSum
  12. If(IsInRegion[A, poly3], 1, If[IsInRegion[B, poly3], 2, If[IsInRegion[C, poly3], 3, If[IsInRegion[D, poly3], 4, If[IsInRegion[E, poly3], 5, If[IsInRegion[F, poly3], 6, If[IsInRegion[G, poly3], 7, If[IsInRegion[H, poly3], 8, If[IsInRegion[I, poly3], 9, 0]]]]]]]]) → threeSum
  13. Min({side1, side2, side3}) → shortestSide
  14. Max({side1, side2, side3}) → longestSide
  15. Element(Remove[{side1, side2, side3}, {longestSide, shortestSide}], 1) → middleSide
  16. Point({5 - ((5 * longestSide / 98) * side1slider), -5}) → bottomLeft
  17. Circle(bottomLeft, (shortestSide * 10 / 98)) → leftSideCircle
  18. Point({5 + ((5 * longestSide / 98) * side1slider), -5}) → bottomRight
  19. Segment(bottomLeft, bottomRight) → bottomSide
  20. Intersect(leftSideCircle, bottomSide) → noIntersectionPoint_1, Q
  21. Circle(bottomRight, (middleSide * 10 / 98)) → rightSideCircle
  22. Intersect(leftSideCircle, rightSideCircle) → intersectionPoint_1, intersectionPoint_2, ,
  23. If(y(intersectionPoint_1) > y(intersectionPoint_2), intersectionPoint_1, intersectionPoint_2) → intersectionPoint
  24. Polygon((0, 0), (0.9, 0), 4) → poly1
  25. Polygon((0, 1), (0.9, 1), 4) → poly4
  26. Polygon((0, 2), (0.9, 2), 4) → poly7
  27. Mod(onesPlace, 10) → SAone
  28. Mod(tensPlace + Div[onesPlace, 10], 10) → SAten
  29. Div(onesPlace, 10) → SAtensCarry
  30. Div(tensPlace + Div[onesPlace, 10], 10) → SAhundredsCarry
  31. Polygon(L, M, N, O) → q1, l, m, n, o
  32. Segment(bottomLeft, (bottomLeft * (1 - otherSidesTimer)) + (If[Defined[intersectionPoint], intersectionPoint, noIntersectionPoint_1] * otherSidesTimer)) → leftSide
  33. Intersect(rightSideCircle, bottomSide) → noIntersectionPoint_2, P
  34. Segment(bottomRight, (bottomRight * (1 - otherSidesTimer)) + (If[Defined[intersectionPoint], intersectionPoint, noIntersectionPoint_2] * otherSidesTimer)) → rightSide
  35. Midpoint(bottomSide) → bottomLabelPoint
  36. Circle(bottomLeft, ((shortestSide * 10 / 98) * leftCircleTimer)) → growingLeftCircle
  37. Circle(bottomRight, ((middleSide * 10 / 98) * rightCircleTimer)) → growingRightCircle
  38. Text(longestSide, bottomLabelPoint - (0, 1)) → text10
  39. Text(shortestSide, leftLabelPoint) → text11
  40. Text(middleSide, rightLabelPoint) → text13
  41. Angle(intersectionPoint, bottomLeft, bottomRight) → α
  42. Angle(intersectionPoint, bottomRight, bottomLeft) → β
  43. Angle(bottomRight, intersectionPoint, bottomLeft) → γ

AI 绘图提示语参考

画一个动态几何图形，展示如何根据角度大小分类三角形。包含多个多边形区域，通过判断点位于哪个区域来决定三角形的类型（锐角、直角、钝角）。使用滑块控制三角形边长，动态显示最短边、最长边和中边，并画出对应的圆和线段。计算并标注三个顶点之间的角度，最终形成一个完整的三角形分类演示。
以上提示语为根据原始绘图命令整理而来，仅供参考。