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Triangles and Segments

Triangles and Segments
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2015-11-24 02:00
TriangleCircleAngleGeometric Construction
This example demonstrates the relationships and properties of line segments, angles, circles, and other geometric elements within a triangle. Key math concepts include angles, centroid, orthocenter, medians, circles, reflections, and piecewise functions. It is constructed using commands like Segment, Midpoint, OrthogonalLine, AngularBisector, Line, Angle, Intersect, Circle, and Distance in GeoGebra. Suitable for high school and above students to explore geometric constructions and proofs.

GeoGebra Commands & Parameters

  1. Segment(B, A) → a
  2. Segment(A, C) → b
  3. Segment(C, B) → c
  4. Midpoint(a) → D
  5. Midpoint(b) → E
  6. Midpoint(c) → F
  7. Segment(A, F) → d
  8. Segment(D, C) → e
  9. Segment(B, E) → f
  10. OrthogonalLine(F, c) → g
  11. OrthogonalLine(E, b) → h
  12. OrthogonalLine(D, a) → i
  13. OrthogonalLine(A, c) → j
  14. OrthogonalLine(C, a) → k
  15. OrthogonalLine(B, b) → l
  16. AngularBisector(A, B, C) → m
  17. AngularBisector(B, C, A) → n
  18. AngularBisector(C, A, B) → p
  19. Line(C, c) → t
  20. Line(A, b) → a_1
  21. Line(B, a) → b_1
  22. Angle(A, C, B) → a1
  23. Angle(C, B, A) → β
  24. Angle(B, A, C) → γ
  25. Line(B, c) → c_1
  26. Line(C, b) → d_1
  27. Line(A, a) → e_1
  28. Intersect(n, a) → G
  29. Intersect(p, c) → H
  30. Intersect(m, b) → I
  31. Intersect(j, t) → J
  32. Intersect(l, d_1) → K
  33. Intersect(k, e_1) → L
  34. Segment(C, F) → f_1
  35. Segment(F, B) → g_1
  36. Segment(B, D) → h_1
  37. Segment(D, A) → i_1
  38. Segment(A, E) → j_1
  39. Segment(E, C) → k_1
  40. Angle(C, L, A) → α
  41. Angle(B, K, C) → δ
  42. Angle(A, J, B) → ε
  43. Circle(A, Distance[A, L] + 1) → p_1
  44. Intersect(p_1, e_1, 2) → M
  45. Angle(C, L, M) → ζ
  46. Circle(B, Distance[B, J] + 1) → q_1
  47. Intersect(q_1, c_1, 2) → N
  48. Angle(A, J, N) → η
  49. Circle(C, Distance[C, K] + 1) → r_1
  50. Intersect(r_1, d_1, 2) → O
  51. Angle(B, K, O) → θ
  52. Intersect(j, k) → P
  53. Intersect(m, n) → Q
  54. Intersect(g, h) → R
  55. Intersect(d, e) → S
  56. Circle(B, A, C) → s_1
  57. Segment(S, I) → l_1
  58. Distance(Q, c) → distanceQc
  59. Midpoint(Q, ClosestPoint[c, Q]) →
  60. Circle(Q, distanceQc) → t_1