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Main Elements of a Triangle

Main Elements of a Triangle
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2014-11-05 21:56
TriangleVectorGeometric Construction
In collections Besondere Punkte/Special Points
This example demonstrates the main elements of a triangle, including midpoints, angle bisectors, and altitudes. By simply clicking, you can intuitively understand the geometric properties of a triangle. Commands used include Circle, Intersect, Polygon, LineBisector, AngularBisector, OrthogonalLine, Line, Midpoint, Segment, etc. Suitable for middle school and above students to learn about the geometric properties of triangles.

GeoGebra Commands & Parameters

  1. Circle(B, c) → k
  2. Circle(C, b) → d_1
  3. Intersect(k, d_1, 1) → A
  4. Polygon(A', B, C) → poly1, c_2, a_2, b_5
  5. LineBisector(a_2) → m_{BC}
  6. LineBisector(c_2) → m_{AB}
  7. LineBisector(b_5) → m_{AC}
  8. Intersect(m_{AC}, m_{BC}) → O
  9. AngularBisector(a_2, c_2) → pb_{ac}, b_2
  10. AngularBisector(a_2, b_5) → pb_{ab}, b_3
  11. AngularBisector(b_5, c_2) → pb_{bc}, b_4
  12. Intersect(b_2, b_4) → I
  13. Circle(I, Distance[I, c_2]) → C_{ins}
  14. OrthogonalLine(A', a_2) → h_A
  15. OrthogonalLine(C, c_2) → h_C
  16. OrthogonalLine(B, b_5) → h_B
  17. Intersect(h_C, h_A) → H
  18. Line(B, Midpoint[b_5]) → m_B
  19. Line(A', Midpoint[a_2]) → m_A
  20. Line(C, Midpoint[c_2]) → m_C
  21. Intersect(m_A, m_B) → G
  22. Circle(O, C) → C_{circ}
  23. Line(H, O) → r_{Euler}
  24. Midpoint(c_2) → M_{AB}
  25. Midpoint(b_5) → M_{AC}
  26. Midpoint(a_2) → M_{BC}
  27. Circle(M_{AB}, M_{BC}, M_{AC}) → C_{FB}
  28. Intersect(h_C, c_2) → P_{AB}
  29. Intersect(h_B, b_5) → P_{AC}
  30. Intersect(h_A, a_2) → P_{BC}
  31. Midpoint(H, A') → P_A
  32. Midpoint(H, B) → P_B
  33. Midpoint(H, C) → P_C
  34. Segment(D, E) → a_1
  35. Segment(D, F) → b_1
  36. Segment(D, J) → c_1
  37. Intersect(C_{FB}, r_{Euler}) → P_{EF1}, P_{EF2}
  38. Midpoint(P_{EF1}, P_{EF2}) → C_{F}
  39. Segment(D, K) → e_1
  40. Intersect(pb_{bc}, pb_{ab}) → C_{b}
  41. Intersect(pb_{ac}, pb_{ab}) → C_{a}
  42. Intersect(pb_{bc}, pb_{ac}) → C_{C}
  43. Circle(C_{C}, Distance[C_{C}, c_2]) → Ext_{C}
  44. Circle(C_{b}, Distance[C_{b}, b_5]) → Ext_{b}
  45. Circle(C_{a}, Distance[C_{a}, a_2]) → Ext_{a}
  46. Segment(M_{AB}, M_{BC}) → b_{ac}
  47. Segment(M_{BC}, M_{AC}) → b_{ab}
  48. Segment(M_{AC}, M_{AB}) → b_{bc}
  49. Line(A', C) → r_{AC}
  50. Line(C, B) → r_{BC}
  51. Line(B, A') → r_{AB}
  52. Intersect(k, d_1) → L, M, ,

AI Drawing Prompt Reference

Draw a triangle ABC and its circumcircle, incircle, altitudes, medians, angle bisectors, and Euler line. First, draw the triangle, then its circumcircle and incircle, followed by the altitudes, medians, and angle bisectors, and finally the Euler line.
The prompt above was compiled from the original drawing commands and is for reference only.