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Altitudes and Orthocenter of a Triangle

Altitudes and Orthocenter of a Triangle
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2020-11-22 15:41
TriangleCoordinate GeometryGeometric Construction
This applet demonstrates the altitudes and orthocenter of a triangle. By drawing the altitudes, students can discover the properties of the orthocenter. Key mathematical concepts include altitudes and the orthocenter of a triangle. The construction uses commands such as Segment, OrthogonalLine, Intersect, Angle, Line, and Polygon. Suitable for middle school and above students to learn geometric constructions.

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 the altitudes from each vertex to the opposite side, marking the intersection point as the orthocenter. Connect each foot of the altitudes to the corresponding vertex. Measure and label the angles of the three smaller triangles formed. Also, measure and label the angles between the altitudes from the orthocenter and the sides of the triangle.
The prompt above was compiled from the original drawing commands and is for reference only.