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Orthocenter by Devin Chang

Orthocenter by Devin Chang
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2017-03-09 14:40
TriangleAngleGeometric Construction
This example demonstrates the construction and properties of the orthocenter in a triangle. Key math concepts include perpendicular lines, intersection points, angles, and triangle geometry. Construction highlights the use of commands like Segment, OrthogonalLine, Intersect, Angle, Line, and Polygon in GeoGebra. Suitable for high school mathematics education or for geometry enthusiasts.

GeoGebra Commands & Parameters

  1. Segment(A, B) → a
  2. Segment(B, C) → b
  3. Segment(C, A) → c
  4. OrthogonalLine(C, a) → d
  5. OrthogonalLine(A, b) → e
  6. OrthogonalLine(B, c) → f
  7. Intersect(d, e) → O
  8. Intersect(d, a) → E
  9. Intersect(f, c) → F
  10. Intersect(e, b) → G
  11. Segment(C, E) → g
  12. Segment(B, F) → h
  13. Segment(A, G) → i
  14. Angle(C, E, A) → α
  15. Angle(B, F, C) → β
  16. Angle(A, G, B) → γ
  17. Line(A, B) → j
  18. Intersect(d, j) → D
  19. Segment(C, D) → k
  20. Angle(C, D, B) → δ
  21. Line(B, C) → l
  22. Polygon(A, B, C) → poly1, c_1, a_1, b_1
  23. Intersect(e, l) → H
  24. Segment(A, H) → m
  25. Angle(A, H, C) → ε
  26. Line(C, A) → n
  27. Intersect(f, n) → I
  28. Segment(B, I) → p
  29. Angle(B, I, A) → ζ

AI Drawing Prompt Reference

Draw a triangle and construct perpendicular lines from each vertex to the opposite side, marking the feet of the altitudes and the orthocenter. Connect the feet of the altitudes to the corresponding vertices and label the angles at the vertices. Then, draw the sides of the triangle and the angle bisectors, marking their intersections with the sides. Finally, connect the orthocenter to the vertices and label the relevant angles.
The prompt above was compiled from the original drawing commands and is for reference only.