MathPlotAI Logo MathPlotAI

Pythagoras' Theorem Demonstration

Pythagoras' Theorem Demonstration
Loading the math board and drawing, please wait…
2020-07-01 13:58
TriangleCircleGeometric Construction
This example dynamically demonstrates the relationship between the sides of a right triangle to verify Pythagoras' Theorem. It involves core mathematical concepts such as Pythagoras' Theorem, right triangles, and geometric constructions. The construction utilizes GeoGebra commands and objects including points, segments, circles, squares, vectors, translation, and rotation. It is suitable for middle school students and math enthusiasts to understand the theorem and its applications.

GeoGebra Commands & Parameters

  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 Drawing Prompt Reference

Draw a right triangle and construct squares on its two legs and hypotenuse. Dynamically demonstrate the relationship between the areas of the squares to verify Pythagoras' Theorem, involving points, lines, circles, vectors, rotations, and translations.
The prompt above was compiled from the original drawing commands and is for reference only.