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Demonstration of the Orthocenter by kcletcher2018

Demonstration of the Orthocenter by kcletcher2018
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2017-01-24 00:24
TriangleVectorTrigonometryGeometric Construction
This example demonstrates the geometric properties and construction methods of the orthocenter of a triangle. It involves core mathematical concepts such as perpendicular lines, intersection points, vectors, trigonometric functions, and similar triangles. The construction uses GeoGebra commands/objects like Polygon, OrthogonalLine, Intersect, Segment, and Angle as outlined in the summary. Suitable for high school mathematics teaching or for geometry enthusiasts.

GeoGebra Commands & Parameters

  1. Polygon(A, B, C) → poly1, c, a, b
  2. OrthogonalLine(A, a) → f
  3. OrthogonalLine(B, b) → g
  4. OrthogonalLine(C, c) → h
  5. Intersect(f, g) → D
  6. Intersect(h, c) → E
  7. Intersect(f, a) → F
  8. Intersect(g, b) → G
  9. Segment(A, F) → i
  10. Segment(C, E) → j
  11. Segment(B, G) → k
  12. Angle(D, E, A) → α
  13. Angle(D, G, C) → β
  14. Angle(D, F, B) → γ