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Orthocenter of a Triangle by Jill Brouillard

Orthocenter of a Triangle by Jill Brouillard
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2016-12-01 23:42
TriangleCoordinate GeometryGeometric Construction
This applet demonstrates the orthocenter of a triangle, the point where the three altitudes intersect. Students can discover the properties of the orthocenter through dynamic drawing. Key mathematical concepts include triangles, altitudes, and the orthocenter. Commands used include Segment, OrthogonalLine, Intersect, Angle, Line, and Polygon. Suitable for middle school and above students learning geometric construction.

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