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Orthocenter and Related Properties

Orthocenter and Related Properties
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2015-11-06 02:47
TriangleComplex NumberGeometric Construction
This example demonstrates the orthocenter of a triangle and its related properties, helping to understand the definition and characteristics of the orthocenter through dynamic visualization. Core mathematical concepts include orthocenter, median, angle bisector, complex numbers, statistical characteristics of circles, continuity, and step functions. The construction uses commands like Polygon, Midpoint, Segment, LineBisector, and AngularBisector in GeoGebra. Suitable for high school and above mathematics learners for deepening geometric construction and triangle properties understanding.

GeoGebra Commands & Parameters

  1. Polygon(A, B, C) → poly1, c, a, b
  2. Midpoint(B, C) → D
  3. Midpoint(A, C) → E
  4. Midpoint(A, B) → F
  5. Segment(B, E) → d
  6. Segment(A, D) → e
  7. Segment(C, F) → f
  8. LineBisector(B, C) → g
  9. LineBisector(C, A) → h
  10. LineBisector(A, B) → i
  11. AngularBisector(A, B, C) → j
  12. AngularBisector(B, C, A) → k
  13. AngularBisector(C, A, B) → l