判断三角形相似性 by Walch Education (2)

判断三角形相似性 by Walch Education (2)
几何画板及绘图内容加载中,请稍等……
2013-04-17 02:17
①本范例演示如何通过构造三角形并分析其角度和边长关系来判断三角形是否相似;②涉及的核心数学概念包括三角形相似判定定理、角度和边长的测量与比较;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使用。

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

画两个三角形,通过构造点、线段和圆来展示它们的相似性。首先绘制一个基准三角形,然后在其旁边绘制另一个三角形,通过测量和比较对应边的长度来验证相似性。使用文本标签显示各边长度的比例,并强调这些比例如何支持相似性结论。
以上提示语为根据原始绘图命令整理而来,仅供参考。