MathPlotAI Logo MathPlotAI

Pythagoras Theorem Demonstration by GreenMaths

Pythagoras Theorem Demonstration by GreenMaths
Loading the math board and drawing, please wait…
2014-02-17 00:09
TriangleCoordinate GeometryGeometric Construction
In collections Pythagoras
This example demonstrates Pythagoras' theorem by constructing the relationship between the sides of a right triangle. Key mathematical concepts include right triangles and the Pythagorean theorem. The construction involves using GeoGebra commands such as Segment, Point, Distance, and Polygon. Suitable for middle school and above students and teachers.

GeoGebra Commands & Parameters

  1. Segment(A, C) → ee
  2. Point(ee) → E
  3. Distance(A, E) → dis
  4. Segment(A, B) → hh
  5. Point(hh) → D
  6. Polygon(A, D, E) → P, e_1, a_1, d_1
  7. Polygon(D, G, F, A) → Q, d_2, g_1, f_1, a_2
  8. Midpoint(E, H) → J
  9. Line(D, E) → ii
  10. OrthogonalLine(J, ii) → j
  11. OrthogonalLine(J, j) → k
  12. Line(A, E) → l
  13. Line(E, I) → m
  14. Line(I, H) → n
  15. Line(H, A) → p
  16. Intersect(p, k) → K
  17. Intersect(l, j) → L
  18. Intersect(m, k) → M
  19. Intersect(n, j) → N
  20. Polygon(K, J, L, A) → R, k_1, j_1, l_1, a_3
  21. Polygon(J, M, E, L) → S, j_2, m_1, e_2, l_2
  22. Polygon(N, I, M, J) → T, n_1, i_1, m_2, j_3
  23. Polygon(K, H, N, J) → U, k_2, h_1, n_2, j_4
  24. Translate(J, u) → J'
  25. Translate(M, u) → M'
  26. Translate(E, u) → E'
  27. Translate(L, u) → L'
  28. Polygon(J', M', E', L') → S', j', m', e', l'
  29. Translate(N, v) → N'
  30. Translate(I, v) → I'
  31. Translate(M, v) → M'_1
  32. Translate(J, v) → J'_1
  33. Polygon(N', I', M'_1, J'_1) → T', n', i', m'_1, j'_1
  34. Translate(K, w) → K'
  35. Translate(J, w) → J'_2
  36. Translate(L, w) → L'_1
  37. Translate(A, w) → A'
  38. Polygon(K', J'_2, L'_1, A') → R', k', j'_2, l'_1, a'
  39. Translate(K, z) → K'_1
  40. Translate(H, z) → H'
  41. Translate(N, z) → N'_1
  42. Translate(J, z) → J'_3
  43. Polygon(K'_1, H', N'_1, J'_3) → U', k'_1, h', n'_1, j'_3
  44. Translate(D, q) → D'
  45. Translate(G, q) → G'
  46. Translate(F, q) → F'
  47. Translate(A, q) → A'_1
  48. Polygon(D', G', F', A'_1) → Q', d', g', f', a'_1
  49. OrthogonalLine(E, a_1) → r
  50. OrthogonalLine(D, a_1) → s
  51. Circle(E, a_1) → t
  52. Intersect(t, r, 2) → O
  53. OrthogonalLine(O, s) → b_1
  54. Intersect(s, b_1) → V
  55. Polygon(D, E, O, V) → poly1, d_3, e_3, o_1, v_1

AI Drawing Prompt Reference

Draw a right triangle ABC with A as the right angle. First, draw sides AB and AC, then construct the hypotenuse BC. Next, create a smaller similar triangle DEF with E as the midpoint, where D, E, and F correspond to A, B, and C. Finally, use translation and rotation to create multiple smaller similar triangles, illustrating the Pythagorean theorem.
The prompt above was compiled from the original drawing commands and is for reference only.