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Medians, Centroid, Altitudes, and Orthocenter by 60000693 (2)

Medians, Centroid, Altitudes, and Orthocenter by 60000693 (2)
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2016-12-01 13:06
TriangleCoordinate GeometryGeometric Construction
This example demonstrates the concepts of medians, centroid, altitudes, and orthocenter in a triangle. By constructing the medians, altitudes, and orthocenter of a triangle, one can visually understand the properties of these geometric elements. The commands used include Polygon, Angle, Circle, Intersect, Line, Segment, Distance, and Midpoint. Suitable for middle school and above students to learn triangle geometry.

GeoGebra Commands & Parameters

  1. Polygon(A, B, C) → poly1, c, a, b
  2. Angle(B, A, C) → α
  3. Angle(A, C, B) → β
  4. Angle(C, B, A) → γ
  5. Circle(A, B) → d
  6. Circle(B, A) → e
  7. Intersect(d, e, 2) → D
  8. Intersect(d, e, 1) → E
  9. Line(D, E) → f
  10. Circle(A, C) → g
  11. Circle(C, A) → h
  12. Intersect(g, h, 2) → F
  13. Intersect(g, h, 1) → G
  14. Line(F, G) → i
  15. Circle(C, B) → k
  16. Circle(B, C) → p
  17. Intersect(k, p, 2) → H
  18. Intersect(k, p, 1) → I
  19. Line(H, I) → j
  20. Intersect(f, c) → J
  21. Intersect(i, b) → K
  22. Intersect(j, a) → L
  23. Segment(A, L) → l
  24. Segment(B, K) → m
  25. Segment(J, C) → n
  26. Intersect(l, m) → M
  27. Circle(A, B) → q
  28. Circle(C, B) → r
  29. Intersect(q, r, 2) → N
  30. Line(B, N) → s
  31. Intersect(s, b) → O
  32. Circle(B, A) → t
  33. Circle(C, A) → c_1
  34. Intersect(t, c_1, 2) → P
  35. Line(A, P) → f_1
  36. Intersect(f_1, a) → Q
  37. Segment(B, O) → g_1
  38. Segment(A, Q) → h_1
  39. Circle(A, B) → d_1
  40. Circle(B, C) → e_1
  41. Intersect(d_1, e_1, 2) → R
  42. Line(R, C) → i_1
  43. Intersect(i_1, c) → S
  44. Segment(C, S) → j_1
  45. Angle(N, O, A) → δ
  46. Angle(A, Q, B) → ε
  47. Circle(A, C) → k_1
  48. Circle(B, C) → p_1
  49. Intersect(k_1, p_1, 2) → T
  50. Line(T, C) → l_1
  51. Intersect(l_1, c) → U
  52. Angle(A, U, T) → ζ
  53. Segment(U, C) → m_1
  54. Intersect(s, f_1) → V
  55. Distance(A, M) → AM
  56. Distance(A, M) → distanceAM
  57. Distance(C, M) → distanceCM
  58. Distance(B, A) → distanceBA
  59. Distance(L, A) → distanceLA
  60. Distance(M, l) → distanceMl
  61. Distance(L, M) → distanceLM
  62. Distance(C, J) → distanceCJ
  63. Distance(M, J) → distanceMJ
  64. Distance(B, K) → distanceBK
  65. Distance(B, M) → distanceBM
  66. Distance(B, K) → o
  67. Distance(B, M) → u
  68. Distance(B, K) → v
  69. Distance(M, K) → distanceMK
  70. Distance(B, M) → w
  71. Distance(M, K) → a_1
  72. Distance(B, K) → b_1
  73. Distance(L, A) → n_1
  74. Distance(A, M) → o_1
  75. Distance(L, M) → q_1
  76. Distance(A, Q) → distanceAQ
  77. Distance(A, V) → distanceAV
  78. Distance(V, Q) → distanceVQ
  79. Distance(B, O) → distanceBO
  80. Distance(B, V) → distanceBV
  81. Distance(V, O) → distanceVO
  82. Distance(C, J) → r_1
  83. Midpoint(C, J) →
  84. Distance(C, M) → s_1
  85. Midpoint(C, M) →
  86. Distance(M, J) → t_1
  87. Midpoint(M, J) →
  88. Distance(C, U) → distanceCU
  89. Midpoint(C, U) →
  90. Distance(C, V) → distanceCV
  91. Midpoint(C, V) →
  92. Distance(V, U) → distanceVU
  93. Midpoint(V, U) →

AI Drawing Prompt Reference

Draw a triangle ABC, then construct its three medians, three altitudes, and three perpendicular bisectors, and mark the centroid, orthocenter, and circumcenter. First, draw the triangle, then draw the median from each vertex to the midpoint of the opposite side, next draw the altitude from each vertex to the opposite side, and finally draw the perpendicular bisector from each vertex to the midpoint of the opposite side, and mark their intersections.
The prompt above was compiled from the original drawing commands and is for reference only.