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Orthocenter Triangle

Orthocenter Triangle
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2016-12-01 10:27
TriangleCoordinate GeometryGeometric Construction
This example demonstrates the construction of a triangle's orthocenter and its related triangle. Core math concepts include orthocenter, matrices, fractions, right triangles, and statistical characteristics. It uses GeoGebra commands like Polygon, Line, OrthogonalLine, and Intersect. Suitable for high school geometry education or construction learning.

GeoGebra Commands & Parameters

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

AI Drawing Prompt Reference

Draw a triangle ABC, then construct the altitudes from vertices A, B, and C to the opposite sides, which intersect at points D, E, and F. Construct the perpendicular from side BC to altitude CA, intersecting at point G. Construct the perpendicular from side CA to altitude AB, intersecting at point H. Finally, construct the intersection of altitude AB and altitude BC at point I. These points D, E, F, G, H, and I are the orthocenter and key points of the related triangle.
The prompt above was compiled from the original drawing commands and is for reference only.