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Orthocenter and Related Geometric Constructions

Orthocenter and Related Geometric Constructions
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2019-11-14 21:24
TriangleCoordinate GeometryGeometric Construction
This example demonstrates the geometric properties of a triangle's orthocenter and related constructions. Core math concepts include orthocenter, angle bisector, segment, intersection, perpendicular line, point, and line. Construction highlights from the summary involve commands like Polygon, LineBisector, Segment, Intersect, OrthogonalLine, Point, and Line in GeoGebra. Suitable for high school mathematics teaching or for geometry enthusiasts to understand orthocenter theorems and geometric construction techniques.

GeoGebra Commands & Parameters

  1. Polygon(A, C, B) → t1, b, a, c
  2. LineBisector(b) → f
  3. Segment(A, C) → g
  4. Intersect(f, b) → D
  5. OrthogonalLine(D, b) → h
  6. LineBisector(a) → i
  7. Intersect(i, a) → E
  8. OrthogonalLine(E, a) → j
  9. Segment(C, E) → k
  10. Segment(E, B) → l
  11. OrthogonalLine(E, a) → m
  12. OrthogonalLine(E, a) → n
  13. Intersect(f, h) → F
  14. Intersect(f, h) → G
  15. Intersect(i, j) → H
  16. Intersect(f, h) → I
  17. Intersect(f, h) → J
  18. Intersect(f, h) → K
  19. Intersect(f, h) → L
  20. Intersect(f, h) → M
  21. Intersect(f, h) → N
  22. Intersect(f, h) → O
  23. Point(n) → P
  24. Intersect(f, h) → Q
  25. Intersect(f, h) → R
  26. Intersect(f, h) → S
  27. LineBisector(c) → p
  28. Segment(A, B) → q
  29. Segment(A, B) → r
  30. Segment(A, C) → s
  31. Segment(C, B) → t
  32. LineBisector(c) → d
  33. Point(d) → T
  34. OrthogonalLine(T, c) → e
  35. Point(h) → U
  36. Point(n) → V
  37. Point(h) → W
  38. Point(h) → Z
  39. Line(W, Z) → f_1
  40. Point(n) → A_1
  41. Point(n) → B_1
  42. Line(A_1, B_1) → g_1