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Discover Pythagoras Theorem

Discover Pythagoras Theorem
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2014-11-09 22:22
TriangleCircleCoordinate GeometryGeometric Construction
This example demonstrates the Pythagorean theorem by moving a point, illustrating the relationship between the sides of a right triangle. Core concepts include Pythagoras theorem, right triangles, and coordinate geometry. Constructed using commands like Point, Semicircle, Midpoint, OrthogonalLine, Intersect, Circle, CircleArc, Polygon, Segment in GeoGebra. Suitable for middle school students and above to learn and understand the proof and application of the Pythagorean theorem.

GeoGebra Commands & Parameters

  1. Point(xAxis) → A
  2. Point(xAxis) → B
  3. Semicircle(A, B) → c
  4. Midpoint(A, B) → C
  5. OrthogonalLine(C, xAxis) → a
  6. Intersect(c, a) → D,
  7. Circle(D, 0.1) → d
  8. Intersect(d, c) → E, F, ,
  9. CircleArc(C, F, A) → e
  10. Point(e) → G
  11. Polygon(A, B, G) → mnohoúhelník1, g, a_1, b
  12. Polygon(G, B, 4) → mnohoúhelník2, f, h, i, j, H, I
  13. Polygon(A, G, 4) → mnohoúhelník3, k, l, m, n, J, K
  14. Polygon(B, A, 4) → mnohoúhelník4, p, q, r, s, L, M
  15. Segment(G, H) → t
  16. Segment(B, I) → b_1
  17. Intersect(t, b_1) → N
  18. OrthogonalLine(N, g) → c_1
  19. OrthogonalLine(N, c_1) → d_1
  20. Intersect(d_1, j) → O
  21. Intersect(d_1, h) → P
  22. Intersect(f, c_1) → Q
  23. Intersect(c_1, i) → R
  24. Segment(Q, B) → e_1
  25. Segment(B, H) → f_1
  26. Segment(H, I) → g_1
  27. Segment(I, G) → h_1
  28. Segment(G, Q) → i_1
  29. Segment(Q, N) → j_1
  30. Segment(N, P) → k_1
  31. Segment(N, R) → l_1
  32. Segment(N, O) → m_1
  33. Circle(L, Segment[N, P]) → p_1
  34. Circle(M, Segment[N, Q]) → q_1
  35. Circle(B, Segment[N, Q]) → r_1
  36. Circle(A, Segment[N, Q]) → s_1
  37. Intersect(p_1, r) → S,
  38. Intersect(q_1, s) → T,
  39. Intersect(r_1, g) → U,
  40. Intersect(s_1, q) → V,
  41. Circle(Q, Segment[B, Q]) → t_1
  42. Circle(S, Segment[Q, B]) → c_2
  43. Circle(T, Segment[Q, B]) → d_2
  44. Circle(U, Segment[B, Q]) → e_2
  45. Circle(V, Segment[Q, B]) → f_2
  46. Intersect(t_1, j_1) → W,
  47. Intersect(c_2, r) → Z, A_1
  48. Intersect(d_2, s) → B_1, C_1
  49. Intersect(g, p) → D_1
  50. Intersect(e_2, g) → E_1, F_1
  51. Intersect(e_2, f_2) → G_1, N_1, ,
  52. Intersect(f_2, q) → H_1, I_1
  53. Circle(Z, Segment[B, W]) → g_2
  54. Circle(B_1, Segment[B, W]) → h_2
  55. Circle(F_1, Segment[B, W]) → k_2
  56. Circle(H_1, Segment[B, W]) → p_2
  57. Intersect(c_2, g_2, 2) → J_1
  58. Intersect(d_2, h_2, 2) → K_1
  59. Intersect(e_2, k_2, 2) → L_1
  60. Intersect(f_2, p_2, 2) → M_1
  61. Segment(L, S) → n_1
  62. Segment(S, J_1) → a_2
  63. Segment(J_1, V) → b_2
  64. Segment(V, L) → i_2
  65. Segment(S, M) → j_2
  66. Segment(M, B) → l_2
  67. Segment(B, A) → m_2
  68. Segment(A, L) → n_2
  69. Segment(S, K_1) → q_2
  70. Segment(T, L_1) → r_2
  71. Segment(U, M_1) → s_2
  72. Polygon(L, S, J_1, V) → mnohoúhelník5, l_3, s_3, j_3, v
  73. Polygon(S, M, T, K_1) → mnohoúhelník6, s_4, m_3, t_2, k_3
  74. Polygon(T, B, U, L_1) → mnohoúhelník7, t_3, b_3, u, l_4
  75. Polygon(U, A, V, M_1) → mnohoúhelník8, u_1, a_3, v_1, m_4
  76. Polygon(Q, B, P, N) → mnohoúhelník9, q_3, b_4, p_3, n_3
  77. Polygon(Q, G, O, N) → mnohoúhelník10, q_4, g_3, o, n_4
  78. Polygon(N, P, H, R) → mnohoúhelník11, n_5, p_4, h_3, r_3
  79. Polygon(N, O, I, R) → mnohoúhelník12, n_6, o_1, i_3, r_4
  80. Polygon(M_1, J_1, K_1, L_1) → mnohoúhelník13, m_5, j_4, k_4, l_5
  81. Polygon(A, B, G) → mnohoúhelník14, g_4, a_4, b_5
  82. Segment(A, K) → c_3
  83. Segment(K, J) → d_3
  84. Segment(J, G) → e_3
  85. Segment(G, A) → f_3
  86. Segment(L, M) → c_4

AI Drawing Prompt Reference

Draw a coordinate plane with a horizontal segment as the base of a right triangle. Construct a semicircle with this segment as its diameter, and pick a point on the semicircle to form the right triangle by connecting it to the segment's endpoints. Then, construct squares outward on each of the three sides of the triangle. Add auxiliary lines and intersection points inside the figure to create smaller triangles and quadrilaterals that illustrate the geometric proof of the Pythagorean theorem. Finally, place several circles at key positions for marking or explanatory purposes. The overall figure should clearly show the area relationships among the squares on the three sides.
The prompt above was compiled from the original drawing commands and is for reference only.