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Animated Demonstration of Pythagoras Theorem

Animated Demonstration of Pythagoras Theorem
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2015-10-27 21:29
TriangleTrigonometryGeometric ConstructionSlider AnimationLocus
This example animates the Pythagorean Theorem, which states that in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. Key mathematical concepts include right triangles and the Pythagorean theorem. The construction uses commands such as semicircle, intersect, circle arc, point, segment, mirror, polygon, orthogonal line, rotate, midpoint, and if statement. Suitable for middle school and above students and teachers.

GeoGebra Commands & Parameters

  1. Semicircle(A4, A5) → c
  2. Intersect(c, LineBisector[A4, A5]) → A,
  3. CircleArc(Midpoint[A4, A5], A, A4) → r_1
  4. Point(r_1) → A6
  5. Segment(A6, A5) → b
  6. Mirror(A4, b) → A12
  7. Polygon(A6, A5, 4) → poly2, c_2, b_1, g, h, A9, A10
  8. OrthogonalLine(A12, h) → m
  9. Segment(A10, A5) → j
  10. Intersect(m, j) → A11
  11. Rotate(A6, 90*°, A5) → B8
  12. Segment(A4, A6) → a
  13. Segment(A5, A4) → d
  14. Polygon(A4, A6, 4) → poly1, a_1, c_1, e, f, A7, A8
  15. Segment(A4, A7) → i
  16. Mirror(A12, j) → A13
  17. Segment(A5, A12) → k_1
  18. Segment(A5, A13) → l
  19. Segment(A11, A13) → n
  20. Segment(A11, A12) → p
  21. Polygon(A5, A4, 4) → poly4, b_2, a_2, k, q, B12, B6
  22. Rotate(A11, 90*°, A5) → B7
  23. Midpoint(A4, B6) → O
  24. Rotate(B8, 90*°, O) → B10
  25. Rotate(B10, 90*°, O) → B11
  26. Rotate(B11, 90*°, O) → B13
  27. Rotate(B7, 180*°, O) → B9
  28. Segment(B13, B8) → r
  29. Segment(B8, B10) → s
  30. Segment(B11, B13) → d_1
  31. Segment(B11, A4) → e_1
  32. Segment(B13, B12) → f_1
  33. Segment(B8, B6) → g_1
  34. Segment(B10, A5) → h_1
  35. Segment(B7, A5) → j_1
  36. Segment(B9, B12) → p_1
  37. Segment(B10, B11) → q_1
  38. Polygon(C4, C5, C6, C7) → poly3, c2, c3, c4, c5
  39. Polygon(D4, D5, D6) → poly5, d4, d2, d3
  40. Polygon(E4, E5, E6) → poly6, e4, e2, e3
  41. Polygon(F4, F5, F6) → poly7, f4, f2, f3
  42. Polygon(G4, G5, G6) → poly8, g4, g2, g3
  43. Polygon(H4, H5, H6) → poly9, h4, h2, h3
  44. Polygon(I4, I5, I6) → poly10, i4, i2, i3
  45. If(time < C$2, C4, If[(C$2 ≤ time) ∧ (time < C$3), C4 - (time - C$2) * (C4 - C9) / (C$3 - C$2), C9]) → J4
  46. If(time < C$2, C5, If[(C$2 ≤ time) ∧ (time < C$3), C5 - (time - C$2) * (C5 - C10) / (C$3 - C$2), C10]) → J5
  47. If(time < C$2, C6, If[(C$2 ≤ time) ∧ (time < C$3), C6 - (time - C$2) * (C6 - C11) / (C$3 - C$2), C11]) → J6
  48. If(time < C$2, C7, If[(C$2 ≤ time) ∧ (time < C$3), C7 - (time - C$2) * (C7 - C12) / (C$3 - C$2), C12]) → J7
  49. If(time < D$2, D4, If[(D$2 ≤ time) ∧ (time < D$3), D4 - (time - D$2) * (D4 - D9) / (D$3 - D$2), D9]) → K4
  50. If(time < D$2, D5, If[(D$2 ≤ time) ∧ (time < D$3), D5 - (time - D$2) * (D5 - D10) / (D$3 - D$2), D10]) → K5
  51. If(time < D$2, D6, If[(D$2 ≤ time) ∧ (time < D$3), D6 - (time - D$2) * (D6 - D11) / (D$3 - D$2), D11]) → K6
  52. If(time < E$2, E4, If[(E$2 ≤ time) ∧ (time < E$3), E4 - (time - E$2) * (E4 - E9) / (E$3 - E$2), E9]) → L4
  53. If(time < E$2, E5, If[(E$2 ≤ time) ∧ (time < E$3), E5 - (time - E$2) * (E5 - E10) / (E$3 - E$2), E10]) → L5
  54. If(time < E$2, E6, If[(E$2 ≤ time) ∧ (time < E$3), E6 - (time - E$2) * (E6 - E11) / (E$3 - E$2), E11]) → L6
  55. If(time < F$2, F4, If[(F$2 ≤ time) ∧ (time < F$3), F4 - (time - F$2) * (F4 - F9) / (F$3 - F$2), F9]) → M4
  56. If(time < F$2, F5, If[(F$2 ≤ time) ∧ (time < F$3), F5 - (time - F$2) * (F5 - F10) / (F$3 - F$2), F10]) → M5
  57. If(time < F$2, F6, If[(F$2 ≤ time) ∧ (time < F$3), F6 - (time - F$2) * (F6 - F11) / (F$3 - F$2), F11]) → M6
  58. If(time < G$2, G4, If[(G$2 ≤ time) ∧ (time < G$3), G4 - (time - G$2) * (G4 - G9) / (G$3 - G$2), G9]) → N4
  59. If(time < G$2, G5, If[(G$2 ≤ time) ∧ (time < G$3), G5 - (time - G$2) * (G5 - G10) / (G$3 - G$2), G10]) → N5
  60. If(time < G$2, G6, If[(G$2 ≤ time) ∧ (time < G$3), G6 - (time - G$2) * (G6 - G11) / (G$3 - G$2), G11]) → N6
  61. If(time < H$2, H4, If[(H$2 ≤ time) ∧ (time < H$3), H4 - (time - H$2) * (H4 - H9) / (H$3 - H$2), H9]) → O4
  62. If(time < H$2, H5, If[(H$2 ≤ time) ∧ (time < H$3), H5 - (time - H$2) * (H5 - H10) / (H$3 - H$2), H10]) → O5
  63. If(time < H$2, H6, If[(H$2 ≤ time) ∧ (time < H$3), H6 - (time - H$2) * (H6 - H11) / (H$3 - H$2), H11]) → O6
  64. If(time < I$2, I4, If[(I$2 ≤ time) ∧ (time < I$3), I4 - (time - I$2) * (I4 - I9) / (I$3 - I$2), I9]) → P4
  65. If(time < I$2, I5, If[(I$2 ≤ time) ∧ (time < I$3), I5 - (time - I$2) * (I5 - I10) / (I$3 - I$2), I10]) → P5
  66. If(time < I$2, I6, If[(I$2 ≤ time) ∧ (time < I$3), I6 - (time - I$2) * (I6 - I11) / (I$3 - I$2), I11]) → P6
  67. Polygon(J4, J5, J6, J7) → poly11, j4, j5, j6, j7
  68. Polygon(K4, K5, K6) → poly12, k6, k4, k5
  69. Polygon(L4, L5, L6) → poly13, l6, l4, l5
  70. Polygon(M4, M5, M6) → poly14, m6, m4, m5
  71. Polygon(N4, N5, N6) → poly15, n6, n4, n5
  72. Polygon(O4, O5, O6) → poly16, o6, o4, o5
  73. Polygon(P4, P5, P6) → poly17, p6, p4, p5
  74. Polygon(C9, C10, C11, C12) → poly18, c9, c10, c11, c12
  75. Polygon(D9, D10, D11) → poly19, d11, d9, d10
  76. Polygon(E9, E10, E11) → poly20, e11, e9, e10
  77. Polygon(F9, F10, F11) → poly21, f11, f9, f10
  78. Polygon(G9, G10, G11) → poly22, g11, g9, g10
  79. Polygon(H9, H10, H11) → poly23, h11, h9, h10
  80. Polygon(I9, I10, I11) → poly24, i11, i9, i10

AI Drawing Prompt Reference

Draw a right triangle ABC with AB as the hypotenuse. Use rotation and mirroring to construct three smaller similar triangles, each with an area equal to the square of one of the legs of the original triangle. Adjust the size of the triangle using a slider to observe changes in the area relationships.
The prompt above was compiled from the original drawing commands and is for reference only.