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Triangle Orthocenter Demonstration

Triangle Orthocenter Demonstration
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2019-11-14 20:32
TriangleTrigonometryGeometric Construction
This example demonstrates the geometric properties and construction methods of a triangle's orthocenter. It involves core math concepts like orthocenter, sine theorem, quadratic equations, angle calculations, piecewise functions, and natural numbers. The construction uses GeoGebra commands such as Polygon, OrthogonalLine, and Segment. Suitable for high school mathematics teaching and geometric construction learning.

GeoGebra Commands & Parameters

  1. Polygon(A, B, C) → t1, c, a, b
  2. OrthogonalLine(B, b) → f
  3. OrthogonalLine(A, a) → g
  4. OrthogonalLine(C, c) → h
  5. Segment(A, B) → i
  6. Segment(C, B) → j
  7. Segment(C, A) → k
  8. Polygon(E, F, G) → t2, g_1, e, f_1
  9. OrthogonalLine(F, f_1) → l
  10. OrthogonalLine(E, e) → m
  11. OrthogonalLine(G, g_1) → n
  12. Segment(F, G) → p
  13. Segment(E, G) → q
  14. Segment(E, F) → r
  15. Polygon(H, I, J) → t3, j_1, h_1, i_1
  16. OrthogonalLine(H, h_1) → s
  17. OrthogonalLine(J, j_1) → t
  18. OrthogonalLine(I, i_1) → d
  19. Segment(H, J) → k_1
  20. Segment(I, J) → l_1
  21. Segment(I, H) → m_1