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勾股定理直角验证练习

勾股定理直角验证练习
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2024-09-26 21:28
测试改名0角几何作图
所属专题 Satz des Pythagoras - Einführung
本范例通过交互练习帮助学生检验任意三角形是否为直角三角形。核心数学概念是勾股定理的逆定理：如果一个三角形两边的平方和等于第三边的平方，则该三角形为直角三角形。作图要点：利用Point命令绘制随机三角形顶点，Polygon命令构造三角形，If命令实现条件判断，通过Textfield和输入框接收学生答案，利用Shuffle和Element命令实现题目随机抽取。适合7-8年级学生练习勾股定理逆应用，培养数形结合能力。

GeoGebra 命令及参数

  1. Shuffle(1…numberOfQuestions) → randomQuestions, {3, 2, 6, 7, 8, 5, 4, 1}
  2. Element(randomQuestions, Mod[Max[0, questionCount - 1], Length[randomQuestions]] + 1) → randomQuestion
  3. Element(allQuestions, Mod[Max[0, randomQuestion - 1], Length[allQuestions]] + 1) → actualQuestion
  4. Element(actualQuestion, 1) → randomNumber1
  5. Element(actualQuestion, 2) → randomNumber2
  6. Element(actualQuestion, 3) → randomNumber3
  7. IndexOf(Max[{randomNumber1, randomNumber2, randomNumber3}], actualQuestion) → numberHypotenuse
  8. Element({1, 2, 3} \ {numberHypotenuse}, 1) → numberKathete1
  9. Element({1, 2, 3} \ {numberHypotenuse}, 2) → numberKathete2
  10. Element(actualQuestion, numberKathete1) → valueKathete1
  11. Element(actualQuestion, numberKathete2) → valueKathete2
  12. Element(actualQuestion, numberHypotenuse) → valueHypotenuse
  13. Element(actualQuestion, 5) → isRechtwinklig
  14. Textfield(inputA) → inputBoxA
  15. Shuffle(1…24) → randomLettersNumbers, {14, 7, 5, 4, 6, 13, 10, 12, 20, 8, 22, 15, 19, 18, 23, 1, 9, 2, 11, 17, 3, 21, 16, 24}
  16. Element(randomLettersNumbers, Mod[Max[0, questionCount - 1], Length[randomLettersNumbers]] + 1) → actualRandomLettersNumber
  17. Element(randomLetters, actualRandomLettersNumber + 0) → randomLetter1
  18. Element(randomLetters, actualRandomLettersNumber + 1) → randomLetter2
  19. Element(randomLetters, actualRandomLettersNumber + 2) → randomLetter3
  20. Element(actualQuestion, 4) → actualEinheit
  21. Textfield(inputB) → inputBoxB
  22. Take(randomLetters, actualRandomLettersNumber, actualRandomLettersNumber + 2) → actualRandomLetters
  23. Element(actualRandomLetters, numberHypotenuse) → textHypotenuse
  24. Element(actualRandomLetters, numberKathete1) → textKathete1
  25. Element(actualRandomLetters, numberKathete2) → textKathete2
  26. Conic(schnurA, schnurB, schnurC, schnurD, schnurE) → schnur
  27. Element(allDreieckFaktors, randomQuestion) → actualDreieckFaktor
  28. Point(Circle[dreieckA, valueKathete1]) → dreieckB
  29. Point(Circle[dreieck1A, (Element[allQuestions(1), 1] * Element[allDreieckFaktorsKlein, 1])]) → dreieck1B
  30. Point(Circle[dreieck2A, (Element[allQuestions(2), 1] * Element[allDreieckFaktorsKlein, 2])]) → dreieck2B
  31. Point(Circle[dreieck3A, (Element[allQuestions(3), 1] * Element[allDreieckFaktorsKlein, 3])]) → dreieck3B
  32. Point(Circle[dreieck4A, (Element[allQuestions(4), 1] * Element[allDreieckFaktorsKlein, 4])]) → dreieck4B
  33. Point(Circle[dreieck5A, (Element[allQuestions(5), 1] * Element[allDreieckFaktorsKlein, 5])]) → dreieck5B
  34. Point(Circle[dreieck6A, (Element[allQuestions(6), 1] * Element[allDreieckFaktorsKlein, 6])]) → dreieck6B
  35. Point(Circle[dreieck7A, (Element[allQuestions(7), 1] * Element[allDreieckFaktorsKlein, 7])]) → dreieck7B
  36. Point(Circle[dreieck8A, (Element[allQuestions(8), 1] * Element[allDreieckFaktorsKlein, 8])]) → dreieck8B
  37. Point(Semicircle[dreieckStart1A, dreieckStart1B]) → dreieckStart1C
  38. Point(Semicircle[dreieckStart2A, dreieckStart2B]) → dreieckStart2C
  39. Polygon(Dilate[dreieckA, actualDreieckFaktor, dreieckA], Dilate[dreieckB, actualDreieckFaktor, dreieckA], Dilate[dreieckC, actualDreieckFaktor, dreieckA]) → dreieckKlein, dreieckKlein1, dreieckKlein2, dreieckKlein3
  40. If(chk1a1, Corner[chk1a1, 1], If[chk1a2, Corner[chk1a2, 1], If[chk1a3, Corner[chk1a3, 1], (0, -1)]]) → rectangleFeedback1aStart

AI 绘图提示语参考

画一个交互式几何练习，展示勾股定理的逆定理应用。随机生成一个三角形，用不同大小的三个圆分别表示三边，圆心位于顶点。根据勾股定理逆定理，如果三边长度满足最长边的平方等于另外两边平方和，则三角形为直角三角形。用文本框让学生输入判断结果，并显示正确与否的反馈。
以上提示语为根据原始绘图命令整理而来，仅供参考。