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Pythagorean Theorem Proof by GeoGebra Materials Team

Pythagorean Theorem Proof by GeoGebra Materials Team
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2015-10-06 17:03
TriangleCoordinate GeometryGeometric Construction
This example demonstrates the Pythagorean Theorem through geometric dissection. It involves concepts of right triangles and distance. Commands used include Segment, Point, Distance, Polygon, Midpoint, Line, OrthogonalLine, Intersect, Translate. Suitable for middle school and above students to learn geometric proofs.

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

AI Drawing Prompt Reference

Draw a right triangle with one horizontal and one vertical leg. Pick a point on the hypotenuse and drop perpendiculars to both legs, dividing the triangle into two smaller right triangles and a rectangle. Then construct a square outward on the hypotenusehol, and dissect that square by translating and rotating pieces into four congruent right triangles and a central smaller square, illustrating the Pythagorean theorem by dissection. Use dashed lines or distinct colors for translated parts.
The prompt above was compiled from the original drawing commands and is for reference only.