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The Orthocenter Demo by BacchusRas

The Orthocenter Demo by BacchusRas
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2015-03-05 22:22
TriangleAngleGeometric Construction
This example demonstrates the geometric properties and construction method of the orthocenter in a triangle. It involves core mathematical concepts such as perpendicular lines, intersection points, angles, geometric transformations, and the cosine rule. The construction uses GeoGebra commands like Polygon, OrthogonalLine, Intersect, and Angle. 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) → d
  3. OrthogonalLine(B, b) → e
  4. OrthogonalLine(C, c) → f
  5. Intersect(d, e) → D
  6. Angle(b, e) → α
  7. Angle(a, d) → β
  8. Angle(c, f) → γ

AI Drawing Prompt Reference

Draw a triangle ABC, then draw a perpendicular line from point A with AB as the radius, and draw another perpendicular line from point B with BC as the radius. The intersection of these two perpendicular lines is the orthocenter D of the triangle. Then measure the angle α between angle B and angle D, the angle β between angle A and angle D, and the angle γ between angle C and angle D.
The prompt above was compiled from the original drawing commands and is for reference only.