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Triangle Parts: Perpendicular Bisectors, Altitudes, etc.

Triangle Parts: Perpendicular Bisectors, Altitudes, etc.
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2019-01-02 10:46
TriangleCircleGeometric Construction
In collections Parts of a Triangle
This example demonstrates the geometric properties and relationships of triangle components such as perpendicular bisectors, altitudes, and angle bisectors. Key math concepts include perpendicular lines, altitudes, angle bisectors, midpoints, distances, and circles. Construction highlights GeoGebra commands like Polygon, OrthogonalLine, Intersect, Segment, Angle, Midpoint, Distance, LineBisector, Circle, and Line. Suitable for high school and above mathematics learners to explore triangle geometry and constructions.

GeoGebra Commands & Parameters

  1. Polygon(R, M, T) → t4, t_1, r_1, s_1
  2. OrthogonalLine(M, s_1) → d
  3. Intersect(d, s_1) → U
  4. Segment(M, U) → e
  5. Angle(T, U, M) → α
  6. Segment(V, W) → f_1
  7. Midpoint(V, W) → Z
  8. OrthogonalLine(Z, f_1) → i_1
  9. Distance(Z, V) → distanceZV
  10. Distance(W, Z) → distanceWZ
  11. Segment(V, S) → m_1
  12. Segment(S, W) → q_1
  13. OrthogonalLine(Z, f_1) → j_1
  14. Intersect(j_1, q_1) → H_1
  15. Segment(Z, H_1) → k_1
  16. Angle(W, Z, H_1) → β
  17. LineBisector(f_1) → f
  18. Intersect(f, m_1) → A
  19. Segment(Z, A) → g
  20. Angle(A, Z, V) → γ
  21. Segment(Z, V) → h
  22. Segment(Z, W) → i
  23. Polygon(B, C, D) → t1, d_1, b, c
  24. LineBisector(c) → j
  25. LineBisector(d_1) → k
  26. LineBisector(b) → l
  27. Intersect(j, d_1) → E
  28. Intersect(j, c) → F
  29. Intersect(k, d_1) → G
  30. Intersect(k, c) → H
  31. Intersect(l, b) → I
  32. Intersect(l, c) → J
  33. Intersect(j, b) → K
  34. Intersect(k, b) → L
  35. Intersect(l, d_1) → M_1
  36. Intersect(j, k) → Circumcenter
  37. Angle(C, I, J) → δ
  38. Angle(D, F, K) → ε
  39. Angle(L, G, C) → ζ
  40. Angle(H, G, C) → η
  41. Angle(D, F, E) → θ
  42. Angle(M_1, I, D) → ι
  43. Circle(Circumcenter, C) → p
  44. Polygon(S_1, O, P) → t2, p_1, n, o
  45. OrthogonalLine(P, p_1) → m
  46. Intersect(m, p_1) → Q
  47. OrthogonalLine(O, o) → q
  48. Intersect(q, o) → A_1
  49. OrthogonalLine(S_1, n) → r
  50. Intersect(r, n) → B_1
  51. Intersect(m, q) → Orthocenter
  52. Angle(P, Q, O) → κ
  53. Angle(S_1, B_1, P) → λ
  54. Angle(P, A_1, O) → μ
  55. Segment(Q, Orthocenter) → s
  56. Segment(B_1, Orthocenter) → t
  57. Segment(A_1, Orthocenter) → a
  58. Line(R, T) → g_1
  59. OrthogonalLine(M, g_1) → h_1
  60. Intersect(g_1, h_1) → N
  61. Angle(M, N, R) → ν
  62. Segment(M, N) → l_1