判断三角形相似性

判断三角形相似性
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2014-11-05 01:35
①本范例演示如何判断两个三角形是否相似;②涉及的核心数学概念包括相似三角形的判定定理、角度关系、边长比例;③作图要点——从下方『构造摘要』提炼用到了 Point(点)、Segment(线段)、Polygon(多边形)、Circle(圆)、Intersect(交点)、TableText(表格文本)等 GeoGebra 命令/对象;④适合高中数学学生学习和教师教学演示。

GeoGebra 命令及参数

  1. Point(xAxis) → windowPosition
  2. Segment(sizeLeft, sizeRight) → sizeLine
  3. Point(sizeLine) → sizePoint
  4. Polygon((x(windowPosition), y(Corner[1])), Corner[2], Corner[3], (x(windowPosition), y(Corner[4]))) → window, windowBottom, windowRight, windowTop, windowleft
  5. Segment(sliderTop, sliderBottom) → sliderLine
  6. Point(sliderLine) → sliderPoint
  7. Point(Circle[A, 4.5]) → B_{build}
  8. Segment(A, B_{build}) → a
  9. Circle(B_{build}, 4.5) → c
  10. Circle(A, 6) → d
  11. Intersect(d, c) → C_1, C, ,
  12. Point(Circle[D, (size * 6)]) → E
  13. Segment(D, E) → b
  14. Circle(E, (size * 7.5)) → e
  15. Circle(D, (size * 10)) → f
  16. Intersect(e, f) → F_1, F, ,
  17. Segment(B_{build}, C) → g
  18. Segment(C, A) → h
  19. Segment(D, F) → i
  20. Segment(E, F) → j
  21. Segment(A, B_{build}) → k
  22. Segment(B_{build}, C) → l
  23. Segment(C, A) → m
  24. Segment(D, E) → n
  25. Segment(E, F) → p
  26. Segment(F, D) → q
  27. TableText({{"\frac{\textcolor{#000099}{\mathit{AB}}}{\textcolor{#000099}{\mathit{DE}}}", "=", "\frac{4.5}{6}", "=", "\frac{3}{4}"}, {"\frac{\textcolor{#006633}{\mathit{BC}}}{\textcolor{#006633}{\mathit{EF}}}", "=", "\frac{4.5}{7.5}", "=", "\frac{3}{5}"}, {"\frac{\textcolor{#FF0000}{\mathit{AC}}}{\textcolor{#FF0000}{\mathit{DF}}}", "=", "\frac{6}{10}", "=", "\frac{3}{5}"}}, "rcccl") → text3
  28. TableText({{"\frac{\textcolor{#000099}{\mathit{AB}}}{\textcolor{#000099}{\mathit{DE}}}", "=", (("\frac{4.5}{" * b) * "}"), "=", FractionText[shortest]}, {"\frac{\textcolor{#006633}{\mathit{BC}}}{\textcolor{#006633}{\mathit{EF}}}", "=", (("\frac{4.5}{" * j) * "}"), "=", FractionText[middle]}, {"\frac{\textcolor{#FF0000}{\mathit{AC}}}{\textcolor{#FF0000}{\mathit{DF}}}", "=", (("\frac{6}{" * i) * "}"), "=", FractionText[longest]}}, "rcccl") → text4

AI 绘图提示语参考

画一个几何图形,展示两个三角形相似性的判定。包含一个坐标系,两个三角形通过顶点连接,并有辅助圆和线段。标注三组对应边的比例,用不同颜色区分,并显示比例相等的结论,强调相似三角形的边长比例关系。
以上提示语为根据原始绘图命令整理而来,仅供参考。