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Orthocenter and Polygon Construction

Orthocenter and Polygon Construction
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2017-01-24 03:36
VectorFunctionTrigonometryGeometric Construction
This example demonstrates the geometric properties of the orthocenter in polygons (especially trapezoids) and the intersection points between function graphs; Core math concepts include orthogonal lines, vectors, function graphs, roots, and set theory; Construction highlights use of Polygon, OrthogonalLine, Intersect, Segment, Angle commands in GeoGebra; Suitable for high school and above students to understand the interaction between spatial geometry and function graphs.

GeoGebra Commands & Parameters

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

AI Drawing Prompt Reference

Draw an arbitrary triangle. From each vertex, construct a perpendicular line to the opposite side, marking the foot of each perpendicular on that side (or its extension). Connect each vertex to its corresponding foot, forming three altitude segments. At each foot, draw a small right-angle symbol between the altitude and the side. The three altitudes intersect at a single common point, the orthocenter. Clearly show the triangle, the three altitudes, the feet, the right-angle marks, and the orthocenter.
The prompt above was compiled from the original drawing commands and is for reference only.