MathPlotAI Logo MathPlotAI

A Right-Angle Request

A Right-Angle Request
Loading the math board and drawing, please wait…
2025-03-27 21:36
TriangleCoordinate GeometryGeometric Construction
In collections Satz des Pythagoras - Einführung
A right-angle request! In this task, a calculator is recommended. This task is suitable for 7-8 grade students, helping them check if a triangle is a right-angled triangle by reversing the Pythagorean theorem. Using GeoGebra, students can interactively explore the properties of right-angled triangles. The task uses various GeoGebra commands and objects, including SelectedIndex, If, Zip, Join, etc. It is suitable for learning coordinate geometry and geometric construction.

GeoGebra Commands & Parameters

  1. SelectedIndex(DropDown7) → input7
  2. SelectedIndex(DropDown6) → input6
  3. If(rechtwinkelig, 2, 3) → sol7
  4. If(rechtwinkelig, 2, 3) → sol6
  5. Zip(Text[(("$\textsf{" * m) * "²\vphantom{Öj}}$")], m, listVariables) → listVariablesSquare
  6. Join({{"$\textsf{~~~\vphantom{Öj}}$"}, listVariablesSquare}) → DropDown2
  7. SelectedIndex(DropDown2) → input2
  8. Join({{"$\textsf{~~~\vphantom{Öj}}$"}, listVariablesSquare}) → DropDown1
  9. SelectedIndex(DropDown1) → input1
  10. Join({{"$\textsf{~~~\vphantom{Öj}}$"}, listVariablesSquare}) → DropDown3
  11. SelectedIndex(DropDown3) → input3
  12. SelectedIndex(DropDown0) → input0
  13. Textfield(input4) → Eingabefeld4
  14. Textfield(input5) → Eingabefeld5
  15. Shuffle(Sequence[Random[0, 10], i, 1, 100]) → randomNosForX, {6, 2, 5, 6, 0, 5, 7, 8, 0, 6, 1, 8, 9, 2, 0, 7, 3, 0, 7, 5, 7, 0, 2, 6, 7, 3, 1, 4, 4, 0, 2, 10, 4, 3, 7, 7, 4, 4, 6, 7, 3, 8, 6, 5, 3, 6, 10, 4, 1, 1, 3, 0, 10, 6, 1, 10, 3, 5, 2, 10, 8, 3, 9, 10, 0, 10, 6, 1, 7, 6, 0, 6, 4, 8, 0, 2, 3, 1, 3, 10, 6, 10, 1, 10, 4, 3, 1, 2, 7, 5, 6, 3, 2, 9, 8, 1, 7, 2, 3, 2}
  16. Element(randomNosForX, Mod[questionCount, 100] + 1) → numX
  17. Shuffle(Sequence[Random[0, 10], i, 1, 100]) → randomNosForY, {4, 1, 2, 0, 0, 2, 5, 7, 3, 8, 8, 10, 10, 7, 3, 3, 0, 0, 10, 3, 7, 2, 2, 9, 7, 0, 8, 1, 8, 3, 0, 3, 3, 4, 5, 0, 10, 10, 5, 7, 1, 8, 10, 9, 6, 7, 1, 3, 6, 10, 3, 5, 5, 10, 4, 9, 9, 6, 7, 8, 2, 7, 0, 4, 9, 1, 4, 3, 0, 9, 5, 4, 3, 1, 9, 9, 5, 5, 1, 3, 2, 5, 7, 9, 9, 6, 10, 3, 7, 10, 6, 7, 3, 8, 3, 3, 9, 0, 9, 5}
  18. Element(randomNosForY, Mod[questionCount, 100] + 1) → numY
  19. Append(true, Sequence[If[randomNosForX(i) ≟ randomNosForX(i - 1), false, true], i, 2, 100]) → stayX
  20. Append(true, Sequence[If[randomNosForY(i) ≟ randomNosForY(i - 1), false, true], i, 2, 100]) → stayY
  21. Remove(Sequence[If[stayX(i), randomNosForX(i), 0], i, 1, 100], Sequence[0, i, 1, 100]) → randomNosForXwithoutRepeat
  22. Element(randomNosForXwithoutRepeat, Mod[questionCount, Length[randomNosForXwithoutRepeat]] + 1) → numXwithoutRepeat
  23. Element({2, 3}, part) → tries
  24. Join(Sequence[Shuffle[Sequence[1, maxexnum]], m, 1, floor(110 / maxexnum)]) → listExnum
  25. Sequence(Sort[listNumsAllABC(m), listNumsABCorder(m)], m, 1, 6) → listNumsAll123
  26. If(startpage ∨ endpage, listPosAll(listPosNum(2)), Pos0) → P2
  27. If(startpage ∨ endpage, listPosAll(listPosNum(3)), Pos0) → P3
  28. If(startpage ∨ endpage, listPosAll(listPosNum(4)), Pos0) → P4
  29. If(startpage ∨ endpage, listPosAll(listPosNum(5)), Pos0) → P5
  30. If(startpage ∨ endpage, listPosAll(listPosNum(6)), Pos0) → P6
  31. If(startpage ∨ endpage, listPosAll(listPosNum(1)), Pos0) → P1
  32. Defined((input4 * input5)) → fixedDropDown6
  33. Text("\textsf\scriptsize{nicht rechtwinklig}", P1 + posTextRechtwinkelig, true, true, -1) → TextRechtwinkelig1
  34. Text("\textsf\scriptsize{nicht rechtwinklig}", P2 + posTextRechtwinkelig, true, true, -1) → TextRechtwinkelig2
  35. Text("\textsf\scriptsize{rechtwinklig}", P3 + posTextRechtwinkelig, true, true, -1) → TextRechtwinkelig3
  36. Text("\textsf\scriptsize{rechtwinklig}", P4 + posTextRechtwinkelig, true, true, -1) → TextRechtwinkelig4
  37. Text("\textsf\scriptsize{rechtwinklig}", P5 + posTextRechtwinkelig, true, true, -1) → TextRechtwinkelig5
  38. Text("\textsf\scriptsize{nicht rechtwinklig}", P6 + posTextRechtwinkelig, true, true, -1) → TextRechtwinkelig6
  39. Rotate(A1 + ((listFactors(1), 0) * listNumsAllABC(1, 3)), 46.5°, A1) → B1
  40. Intersect(Circle[A1, (listNumsAllABC(1, 2) * listFactors(1))], Circle[B1, (listNumsAllABC(1, 1) * listFactors(1))], 1) → C1
  41. Rotate(A2 + ((listFactors(2), 0) * listNumsAllABC(2, 3)), 44°, A2) → B2
  42. Rotate(A3 + ((listFactors(3), 0) * listNumsAllABC(3, 3)), -46.5°, A3) → B3
  43. Rotate(A4 + ((listFactors(4), 0) * listNumsAllABC(4, 3)), 46.5°, A4) → B4
  44. Rotate(A5 + ((listFactors(5), 0) * listNumsAllABC(5, 3)), 46.5°, A5) → B5
  45. Rotate(A6 + ((listFactors(6), 0) * listNumsAllABC(6, 3)), 220°, A6) → B6
  46. Intersect(Circle[A2, (listNumsAllABC(2, 2) * listFactors(2))], Circle[B2, (listNumsAllABC(2, 1) * listFactors(2))], 1) → C2
  47. Intersect(Circle[A3, (listNumsAllABC(3, 2) * listFactors(3))], Circle[B3, (listNumsAllABC(3, 1) * listFactors(3))], 1) → C3
  48. Intersect(Circle[A4, (listNumsAllABC(4, 2) * listFactors(4))], Circle[B4, (listNumsAllABC(4, 1) * listFactors(4))], 1) → C4
  49. Intersect(Circle[A5, (listNumsAllABC(5, 2) * listFactors(5))], Circle[B5, (listNumsAllABC(5, 1) * listFactors(5))], 1) → C5
  50. Intersect(Circle[A6, (listNumsAllABC(6, 2) * listFactors(6))], Circle[B6, (listNumsAllABC(6, 1) * listFactors(6))], 1) → C6
  51. Segment(B1, C1) → a1
  52. Segment(B2, C2) → a2
  53. Segment(B3, C3) → a3
  54. Segment(B4, C4) → a4
  55. Segment(B5, C5) → a5
  56. Segment(B6, C6) → a6
  57. Segment(B1, A1) → c1
  58. Segment(B2, A2) → c2
  59. Segment(B3, A3) → c3
  60. Segment(B4, A4) → c4
  61. Segment(B5, A5) → c5
  62. Segment(B6, A6) → c6
  63. Segment(A1, C1) → b1
  64. Segment(A2, C2) → b2
  65. Segment(A3, C3) → b3
  66. Segment(A4, C4) → b4
  67. Segment(A5, C5) → b5
  68. Segment(A6, C6) → b6
  69. Join({Sequence[Segment[Corner[4] + (RasterPixMat * ((k * RasterStepXY), 0)), Corner[4] + (RasterPixMat * ((k * RasterStepXY), RasterMaxY))], k, 0, RasterMaxX / RasterStepXY], Sequence[Segment[Corner[4] + (RasterPixMat * (0, (k * RasterStepXY))), Corner[4] + (RasterPixMat * (RasterMaxX, (k * RasterStepXY)))], k, 0, RasterMaxY / RasterStepXY]}) → RasterStrecken
  70. Join({Sequence[Text[UnicodeToLetter[65 + k], Midpoint[Corner[4] + (RasterPixMat * ((k * RasterStepXY), RasterMaxY)), Corner[4] + (RasterPixMat * (((k + 1) * RasterStepXY), RasterMaxY))], false, true, 0, -1], k, 0, RasterMaxX / RasterStepXY - 1], Sequence[Text[("" * k), Midpoint[Corner[4] + (RasterPixMat * (RasterMaxX, ((k - 1) * RasterStepXY))), Corner[4] + (RasterPixMat * (RasterMaxX, (k * RasterStepXY)))], false, true, 1, 0], k, 1, RasterMaxY / RasterStepXY]}) → RasterBeschriftung
  71. Join({Sequence[Segment[Corner[4] + (RasterPixMat * ((k * RasterStepXY), 0)), Corner[4] + (RasterPixMat * ((k * RasterStepXY), RasterMaxY))], k, RasterMaxX / RasterStepXY, RasterMaxX / RasterStepXY], Sequence[Segment[Corner[4] + (RasterPixMat * (0, (k * RasterStepXY))), Corner[4] + (RasterPixMat * (RasterMaxX, (k * RasterStepXY)))], k, RasterMaxY / RasterStepXY, RasterMaxY / RasterStepXY]}) → RasterAussen

AI Drawing Prompt Reference

Draw an interactive right-angle triangle verification tool interface. There are 6 triangles at different positions on the screen, labeled triangle 1 through triangle 6, each consisting of three vertices. Next to each triangle, there is a dropdown menu for users to select two sides as the legs of a right angle. The interface also includes two input fields for entering numbers and multiple selection dropdowns. When the user makes their selections, the system displays next to each triangle whether it is a right triangle ("rechtwinklig") or not a right triangle ("nicht rechtwinklig") through text. The entire interface is designed for students to interactively verify the converse of the Pythagorean theorem by checking if triangles with given side lengths are right triangles.
The prompt above was compiled from the original drawing commands and is for reference only.