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Orthocenter of a Triangle by MsBuist

Orthocenter of a Triangle by MsBuist
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2017-06-13 04:17
TriangleCoordinate GeometryGeometric Construction
This applet demonstrates the orthocenter of a triangle, which is the point where the three altitudes of a triangle intersect. By drawing the altitudes, students can discover the properties of the orthocenter. Key mathematical concepts include altitudes, orthocenter, and angles. The construction uses commands such as Segment, OrthogonalLine, Intersect, Angle, Line, and Polygon. Suitable for middle school and above students to learn triangle geometry.

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 ABC and construct three altitudes from each vertex to the opposite side, finding their intersection point O as the orthocenter. Then, connect O to each vertex to form new segments. Measure and display the angles between each vertex and the orthocenter.
The prompt above was compiled from the original drawing commands and is for reference only.