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Orthocenter Animation

Orthocenter Animation
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2017-05-19 21:09
TriangleGeometric ConstructionSlider AnimationLocus
This example demonstrates the orthocenter animation of a triangle. The orthocenter is the point where the three altitudes of a triangle intersect. Using GeoGebra commands such as Rotate, Angle, Segment, Ray, Point, Circle, Intersect, etc., the formation process of the orthocenter can be dynamically shown. Suitable for students at junior high school level and above to learn triangle geometry.

GeoGebra Commands & Parameters

  1. Rotate(A, (a * π / 180), B) → A'
  2. Angle(A, B, A') → α
  3. Segment(B, A) → f
  4. Ray(B, A') → g
  5. Point(g) → C
  6. Segment(B, C) → h
  7. Circle(B, b) → c
  8. Intersect(c, f, 1) → D
  9. Intersect(c, h, 1) → E
  10. CircleSector(B, D, E) → d
  11. Segment(C, A) → i
  12. Line(C, A) → j
  13. Line(A, B) → k
  14. OrthogonalLine(C, k) → m
  15. Intersect(m, k) → H
  16. Circle(C, 2) → e
  17. Circle(H, 2) → p
  18. Intersect(e, j, 1) → J
  19. Ray(C, J) → n
  20. Line(C, H) → r
  21. Polygon(B, A, C) → poly1, c_1, b_1, a_1
  22. Angle(C, A, B) → β
  23. Midpoint(f) → I
  24. Angle(A, H, C) → δ
  25. Line(C, B) → l
  26. OrthogonalLine(A, l) → q
  27. Intersect(q, l) → F
  28. Angle(B, F, A) → γ
  29. Intersect(q, r) → G
  30. Segment(C, H) → s
  31. Line(C, H) → t
  32. Circle(C, 2) → d_1
  33. Circle(H, 2) → e_1
  34. Intersect(d_1, t, 1) → L
  35. Intersect(e_1, t) → M, N
  36. Ray(C, L) → f_1
  37. Ray(H, N) → g_1
  38. Segment(C, H) → h_1
  39. Midpoint(C, G) → O
  40. Circle(B, 1) → k_1
  41. Circle(A, 1) → p_1
  42. Intersect(k_1, k, 2) → P
  43. Intersect(p_1, k, 1) → Q
  44. Ray(B, P) → i_1
  45. Ray(A, Q) → j_1
  46. Dilate(B, If[0 < o ≤ 1, 1 - o, 0], I) → B'
  47. Segment(B, B') → l_1
  48. Rotate(B, If[1 < o ≤ 2, ((-(o - 1)) * π), (-π)], I) → B'_1
  49. Rotate(B', If[1 < o ≤ 2, ((-(o - 1)) * π), (-π)], I) → B''
  50. Segment(B'_1, B'') → m_1
  51. Intersect(k_1, l, 2) → K
  52. Circle(C, 2) → q_1
  53. Intersect(q_1, l, 1) → R
  54. Segment(B, C) → n_1
  55. Ray(C, R) → r_1
  56. Ray(B, K) → s_1
  57. Dilate(A, If[2 < o ≤ 3, 3 - o, 0], F) → A'_1
  58. Segment(A, A'_1) → t_1
  59. Dilate(C, If[3 < o ≤ 4, 4 - o, 0], O) → C'
  60. Segment(C, C') → f_2
  61. Dilate(O, If[4 < o ≤ 5, 5 - o, 0], G) → O'
  62. Segment(O, O') → g_2
  63. Dilate(G, If[5 < o ≤ 6, 6 - o, 0], H) → G'
  64. Segment(G, G') → h_2
  65. Rotate(C, If[6 < o ≤ 7, ((-(o - 6)) * π), (-π)], O) → C'_1
  66. Rotate(C', If[6 < o ≤ 7, ((-(o - 6)) * π), (-π)], O) → C''
  67. Segment(C'_1, C'') → i_2
  68. Angle(I, F, O) → ε
  69. Dilate(I, If[8 < o ≤ 9, 9 - o, 0], F) → I'
  70. Dilate(O, If[8 < o ≤ 9, 9 - o, 0], F) → O'_1
  71. Segment(I, I') → j_2
  72. Segment(O, O'_1) → k_2
  73. Line(A, F) → l_2
  74. Line(C, B) → m_2

AI Drawing Prompt Reference

Draw a triangle ABC and dynamically show the formation process of its orthocenter H. First, use rotation and angle calculation to determine the position of point C, then draw the three altitudes of the triangle and find their intersection point, which is the orthocenter H. Finally, rotate and move point B to dynamically show the change in the position of the orthocenter H.
The prompt above was compiled from the original drawing commands and is for reference only.