勾股定理演示 by txywishes

勾股定理演示 by txywishes
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2020-07-01 13:58
①本范例通过动态演示直角三角形三边关系验证勾股定理;②涉及核心数学概念包括勾股定理、直角三角形、几何作图;③构造过程中运用了点、线段、圆、正方形、向量、平移、旋转等GeoGebra命令与对象;④适合初中及以上学生及数学爱好者用于理解勾股定理及其应用。

GeoGebra 命令及参数

  1. PointIn(a) → B
  2. Circle(A, B) → c
  3. Segment(A, B) → sAB
  4. OrthogonalLine(A, sAB) → perpLineA
  5. Intersect(c, perpLineA, 1) → C_1
  6. Polygon(A, B, 4) → sqSmall, f, g, h, i, D, E
  7. Polygon({A, B, D, E}) → sqSmall2
  8. Centroid(sqSmall) → centreSqSmall
  9. Vector(A, C_1) → uAC1
  10. Ray(C_1, uAC1) → horizRay
  11. Point(horizRay) → C
  12. Polygon(B, C, 4) → sqBig, n, p, q, r, H, I
  13. Centroid(sqBig) → centreSqBig
  14. Vector(centreSqSmall, centreSqBig) → vCentreSqSmallToBig
  15. Polygon(C, A, 4) → sqMed, j, k, l, m, F, G
  16. Centroid(sqMed) → centreSqMed
  17. OrthogonalLine(centreSqMed, n) → perpBC
  18. OrthogonalLine(centreSqMed, perpBC) → s
  19. Intersect(perpBC, j) → ptSqMedAC
  20. Intersect(s, m) → ptSqMedCG
  21. Intersect(perpBC, l) → ptSqMedFG
  22. Intersect(s, k) → ptSqMedAF
  23. Vector(centreSqMed, B) → vCentreSqMedToB
  24. Vector(centreSqMed, C) → vCentreSqMedToC
  25. Vector(centreSqMed, I) → vCentreSqMedToI
  26. Vector(centreSqMed, H) → vCentreSqMedToH
  27. Polygon({C, ptSqMedCG, centreSqMed, ptSqMedAC}) → quadC
  28. Polygon({G, ptSqMedFG, centreSqMed, ptSqMedCG}) → quadG
  29. Polygon({F, ptSqMedAF, centreSqMed, ptSqMedFG}) → quadF
  30. Polygon({A, ptSqMedAC, centreSqMed, ptSqMedAF}) → quadA
  31. Translate(quadA, Vector[(paramMoveToC / 100 * vCentreSqMedToC)]) → quadAMove
  32. Translate(quadC, Vector[(paramMoveToB / 100 * vCentreSqMedToB)]) → quadCMove
  33. Translate(quadF, Vector[(paramMoveToH / 100 * vCentreSqMedToH)]) → quadFMove
  34. Translate(sqSmall2, Vector[(paramMoveSmall / 100 * vCentreSqSmallToBig)]) → sqSmall2Move
  35. Translate(quadG, Vector[(paramMoveToI / 100 * vCentreSqMedToI)]) → quadGMove
  36. Angle(C, A, B) → α
  37. Polygon({A, B, C}) → tri
  38. Polygon({B, C, H, I}) → sqBigBg
  39. Textfield(ans) → InputBox1

AI 绘图提示语参考

画一个直角三角形,并在其两条直角边和斜边上分别作正方形。通过动态演示,展示三个正方形的面积关系验证勾股定理,包含点、线、圆、向量、旋转和平移等几何构造,适合理解勾股定理及其应用。
以上提示语为根据原始绘图命令整理而来,仅供参考。