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勾股定理：用不同标记表达直角三角形

勾股定理：用不同标记表达直角三角形
几何画板及绘图内容加载中，请稍等……
2024-09-26 21:28
测试改名0多边形角三角函数几何作图
所属专题 Satz des Pythagoras - Einführung
这个范例演示如何在直角三角形给定条件下，用不同字母标记与符号方式表述勾股定理，并通过交互输入验证答案。核心数学概念包括：直角三角形、勾股定理（a^2+b^2=c^2 的对应关系）、几何元素命名与符号替换、以及对不同标记约定的理解。作图与交互要点来自下方“构造摘要”：使用 Polygon、Segment、Point 与 Angle 来构建直角三角形与角度标识；用 PointIn、IsInRegion 判断点是否落在指定区域；通过 Midpoint 获取中点相关辅助几何；用 Textfield 与 SpeechBubbleLeft 呈现题目输入与解题提示；用 If、SelectedIndex、Element 控制不同题目/步骤的显示与取值；并结合 btnValidate、attemptCount、correctCount、questionCount 记录作答过程。适合7–8年级（或同等水平）课堂练习、分层作业与几何基础巩固，用于训练学生将图形信息转化为代数等式表达的能力。

GeoGebra 命令及参数

  1. Midpoint(Corner[txtq321, 1], Corner[txtq321, 3]) → MP31
  2. Midpoint(Corner[txtq323, 1], Corner[txtq323, 3]) → MP33
  3. Midpoint(Corner[txtq322, 1], Corner[txtq322, 3]) → MP32
  4. IsInRegion(MP31, poly34(1)) → correct321
  5. IsInRegion(MP32, poly31(1)) → correct322
  6. IsInRegion(MP33, poly33(1)) → correct323
  7. Midpoint(Corner[txtq324, 1], Corner[txtq324, 3]) → MP34
  8. IsInRegion(MP34, poly32(1)) → correct324
  9. If(inputa1 ≟ solaSq, inputb1 ≟ solbSq, inputa1 ≟ solbSq, inputb1 ≟ solaSq, inputa1 ≟ sol225, inputb1 ≟ sol1296, inputa1 ≟ sol1296, inputb1 ≟ sol225, inputb1 ≟ solaSq ∨ inputb1 ≟ solbSq ∨ inputb1 ≟ sol225 ∨ inputb1 ≟ sol1296) → correctb1
  10. SelectedIndex(dropdown1) → index1
  11. If(questionCount ≟ 1, correcta1 ∧ correctb1 ∧ correctd1 ∧ correctf1 ∧ correctdd1, questionCount ≟ 5, (¬option41) ∧ (¬option42) ∧ (¬option43) ∧ option44, false, questionCount ≟ 2, correcta2, questionCount ≟ 3 ∧ step3 ≟ 1, correct31, questionCount ≟ 3 ∧ step3 ≟ 2, correct32, questionCount ≟ 4, (¬option41) ∧ (¬option42) ∧ option43 ∧ option44) → correct
  12. Element(randomQuestions, Mod[questionCount, Length[randomQuestions]] + 1) → randomQuestion
  13. Element(randomQuestions, questionCount) → actualQuestion
  14. Textfield(inputd1) → InputBoxd1
  15. Textfield(inputf1) → InputBoxf1
  16. Textfield(input32) → InputBox32
  17. If(questionCount ≟ 1, (¬calculated012) ∧ (¬calculated013) ∧ Defined[inputa1] ∧ Defined[inputb1] ∧ Defined[inputd1] ∧ Defined[inputf1] ∧ index1 ≠ 1, true, questionCount ≟ 2, Defined[inputa2], questionCount ≟ 3 ∧ step3 ≟ 1, selectedq31 ∨ selectedq32 ∨ selectedq33 ∨ selectedq34, questionCount ≟ 3 ∧ step3 ≟ 2, Defined[input32] ∧ (¬calculated032), questionCount ≟ 4 ∨ questionCount ≟ 5, option41 ∨ option42 ∨ option43 ∨ option44) → clickableBtnValidate
  18. If(questionCount ≟ 3 ∧ step3 ≟ 1, (3.72, 6.5), questionCount ≟ 5, (3.2, 7.06), (3.72, 7.06)) → SB0Point
  19. If(step3 ≟ 1, 12, 10.4) → SB3width
  20. If(step3 ≟ 1, 3, 1.25) → SB3height
  21. SpeechBubbleLeft(SB0Point, SBwidthlist(questionCount + 1), SBheightlist(questionCount + 1)) → SB0
  22. Textfield(inputa1) → InputBoxa1
  23. Textfield(inputb1) → InputBoxb1
  24. Textfield(inputc1) → InputBoxc1
  25. Textfield(inpute1) → InputBoxe1
  26. Textfield(inputa2) → InputBoxa2
  27. Polygon(Corner[txtpos33, 1] + (-0.5, -2) + {(0, 0), (0, 6), (12, 6), (12, 0)}) → rectangle3
  28. PointIn(rectangle3) → Point31
  29. PolyLine({Corner[txtq321, 1], Corner[txtq321, 2], Corner[txtq321, 3], Corner[txtq321, 4], Corner[txtq321, 1]}) → seg321
  30. PolyLine({Corner[txtq322, 1], Corner[txtq322, 2], Corner[txtq322, 3], Corner[txtq322, 4], Corner[txtq322, 1]}) → seg322
  31. PolyLine({Corner[txtq323, 1], Corner[txtq323, 2], Corner[txtq323, 3], Corner[txtq323, 4], Corner[txtq323, 1]}) → seg323
  32. Textfield(inputg1) → InputBoxg1
  33. Textfield(inputh1) → InputBoxh1
  34. Textfield(inputi1) → InputBoxi1
  35. Textfield(inputj1) → InputBoxj1
  36. PolyLine({Corner[txtq324, 1], Corner[txtq324, 2], Corner[txtq324, 3], Corner[txtq324, 4], Corner[txtq324, 1]}) → seg324
  37. Angle(Segment[(14, 2.5), (15, 2.5)], Segment[(15, 2.5), (15, 4.5)]) → rightAngle52
  38. Angle(Vertex[Triangle1(1), 3], Vertex[Triangle1(1), 2], Vertex[Triangle1(1), 1]) → rightAngle1
  39. Point(Semicircle[PosFigure41, PosFigure43]) → PosFigure44
  40. Angle(PosFigure43, PosFigure42, PosFigure41) → rightAngle41
  41. Angle(PosFigure41, PosFigure44, PosFigure43) → rightAngle42
  42. Angle(PosTriangle52, PosTriangle51, PosTriangle53) → rightAngle51
  43. If(questionCount ≟ 1, (4.2, 9.15), questionCount ≟ 3 ∧ step3 ≟ 2, (4.2, 9), (4.2, 9), questionCount ≟ 2, (4.2, 8.55), questionCount ≟ 4, (4.2, 8.55), questionCount ≟ 3 ∧ step3 ≟ 1, (4, 10.35), questionCount ≟ 5, (4.2 - 0.65, 10.25)) → PosQuestionText
  44. Segment(Midpoint[Corner[text15, 1], Corner[text15, 4]], Midpoint[Corner[text15, 1], Corner[text15, 4]] + (lengthClickMe * UnitVector[Vector[Midpoint[Corner[text15, 1], Corner[text15, 4]], Midpoint[Corner[txtq32, 2], Corner[txtq32, 3]]]])) → seg32
  45. Segment(Midpoint[Corner[text15, 1], Corner[text15, 4]], Midpoint[Corner[text15, 1], Corner[text15, 4]] + (lengthClickMe * UnitVector[Vector[Midpoint[Corner[text15, 1], Corner[text15, 4]], Midpoint[Corner[txtq33, 2], Corner[txtq33, 3]]]])) → seg33
  46. Segment(Midpoint[Corner[text15, 1], Corner[text15, 4]], Midpoint[Corner[text15, 1], Corner[text15, 4]] + ((facClickMe * lengthClickMe) * UnitVector[Vector[Midpoint[Corner[text15, 1], Corner[text15, 4]], Midpoint[Corner[txtq31, 2], Corner[txtq31, 3]]]])) → seg31
  47. Segment(Midpoint[Corner[text15, 1], Corner[text15, 4]], Midpoint[Corner[text15, 1], Corner[text15, 4]] + ((facClickMe * lengthClickMe) * UnitVector[Vector[Midpoint[Corner[text15, 1], Corner[text15, 4]], Midpoint[Corner[txtq34, 2], Corner[txtq34, 3]]]])) → seg34
  48. Point(Line[PosImgFuchsHappy1, xAxis]) → PosImgFuchsHappy2

AI 绘图提示语参考

绘制一个直角三角形，包含三个边长分别为a、b和c的直角三角形。使用不同的标签表示直角三角形的边，例如a对应于直角三角形的一条直角边，b对应于另一条直角边，c对应于斜边。绘制一个矩形，包含四个点，分别标记为d、e、f和g。在矩形内绘制四个小三角形，分别标记为31、32、33和34。确保每个小三角形的直角标记正确，并且它们的边长与直角三角形的边长相对应。
以上提示语为根据原始绘图命令整理而来，仅供参考。