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Orthocenter of a Triangle by Ayleen Martinez

Orthocenter of a Triangle by Ayleen Martinez
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2019-12-16 05:16
TriangleCoordinate GeometryGeometric Construction
This example demonstrates the orthocenter of a triangle, which is the point where the three altitudes of a triangle intersect. Using GeoGebra commands such as Polygon, Segment, OrthogonalLine, and Intersect, a dynamic triangle can be constructed and the position of the orthocenter can be observed. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. Polygon(B, A, C) → t1, c, b, a
  2. Segment(A, B) → f
  3. Segment(B, C) → g
  4. Segment(C, A) → h
  5. OrthogonalLine(B, b) → i
  6. OrthogonalLine(A, a) → j
  7. OrthogonalLine(C, c) → k
  8. Intersect(k, c) → D
  9. Intersect(j, a) → E
  10. Intersect(i, b) → F
  11. Intersect(i, j) → G
  12. Angle(G, F, C) → β
  13. Angle(C, E, G) → α
  14. Angle(B, D, G) → γ

AI Drawing Prompt Reference

Draw a triangle ABC and connect its vertices to form three sides. Construct the altitudes from each vertex to the opposite side. The intersection of these altitudes is the orthocenter of the triangle. Observe how the orthocenter changes as you move the vertices.
The prompt above was compiled from the original drawing commands and is for reference only.