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Puzzle Proof of the Pythagorean Theorem

Puzzle Proof of the Pythagorean Theorem
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2015-12-01 07:53
TriangleCircleGeometric Construction
In collections GCSE Higher Ch5 Angles & Trigonometry
This example dynamically demonstrates the Pythagorean Theorem, illustrating the relationship between the sides of a right triangle. Core math concepts include right triangles, the Pythagorean Theorem, vectors, rotation, and polygon construction. It uses commands like Line, Point, Rotate, Distance, Polygon, Segment, Angle, Midpoint, Vector, Translate, and Textfield to prove the theorem through rotation and polygon construction, suitable for high school mathematics teaching and geometric proof learning.

GeoGebra Commands & Parameters

  1. Line(Y, Y') → a_2
  2. Point(a_2) → V
  3. Point(a_2) → A
  4. Rotate(V, α, A) → V'
  5. Line(A, V') → b_2
  6. Point(b_2) → C
  7. Distance(C, A) → a
  8. Point(a_2) → B
  9. Distance(C, B) → c
  10. Distance(B, A) → b
  11. Polygon(A, C, 4) → poly2, c_2, d, e, f, D, E
  12. Segment(A, E) → p
  13. Angle(V, A, V') → β
  14. Polygon(C, A, B) → poly1, b_1, c_1, a_1
  15. Polygon(B, A, 4) → poly3, g, h, i, j, F, G
  16. Polygon(C, B, 4) → poly4, k, l, m, n, H, I
  17. Midpoint(a_1) → J
  18. Rotate(C, (-γ_1), J) → C'
  19. Rotate(A, (-γ_1), J) → A'
  20. Rotate(B, (-γ_1), J) → B'
  21. Polygon(C', A', B') → poly1', b', c', a'
  22. Rotate(C, (-γ_2), A) → C'_1
  23. Rotate(A, (-γ_2), A) → A'_1
  24. Rotate(B, (-γ_2), A) → B'_1
  25. Point(p) → K
  26. Vector(A, K) → u
  27. Translate(C'_1, u) → L
  28. Translate(A'_1, u) → M
  29. Translate(B'_1, u) → N
  30. Polygon(L, M, N) → poly5, n_1, l_1, m_1
  31. Midpoint(m_1) → O
  32. Rotate(L, (-γ_3), O) → L'
  33. Rotate(M, (-γ_3), O) → M'
  34. Rotate(N, (-γ_3), O) → N'
  35. Polygon(L', M', N') → poly5', n', l', m'
  36. Midpoint(C, H) → P
  37. Rotate(C, δ_1, P) → C'_2
  38. Rotate(A, δ_1, P) → A'_2
  39. Rotate(B, δ_1, P) → B'_2
  40. Polygon(C'_2, A'_2, B'_2) → poly1'_1, b'_2, c'_2, a'_2
  41. Rotate(C'_2, δ_2, P) → Q
  42. Rotate(A'_2, δ_2, P) → R
  43. Rotate(B'_2, δ_2, P) → S
  44. Polygon(Q, R, S) → poly6, s, q, r
  45. Rotate(Q, δ_3, P) → Q'
  46. Rotate(R, δ_3, P) → R'
  47. Rotate(S, δ_3, P) → S'
  48. Polygon(Q', R', S') → poly6', s', q', r'
  49. Textfield(α) → inputBox1
  50. Segment(A', R) → t
  51. Point(t) → A_1
  52. Vector(A', A_1) → v
  53. Translate(D, v) → D'
  54. Translate(A', v) → A''
  55. Translate(G, v) → G'
  56. Translate(N, v) → N'_1
  57. Polygon(D', A'', G', N'_1) → poly7', d', a'', g', n'_1
  58. Angle(A, C, B) → θ
  59. Angle(A, B, C) → λ

AI Drawing Prompt Reference

Draw a right triangle ABC with A as the right angle. Use rotation and polygon construction to demonstrate the Pythagorean theorem, which states that the square of the hypotenuse is equal to the sum of the squares of the other two sides. First, draw the legs AB and AC, then construct a circle with center C and radius CA. Through rotation and translation, construct several smaller similar triangles and polygons to prove the theorem.
The prompt above was compiled from the original drawing commands and is for reference only.