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Orthocenter of a Triangle by hasulkin2

Orthocenter of a Triangle by hasulkin2
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2014-09-30 04:11
TriangleCoordinate GeometryGeometric Construction
This example demonstrates how to find the orthocenter of a triangle, which is the point where the three altitudes of a triangle intersect. Using GeoGebra commands such as Segment, OrthogonalLine, and Intersect, the properties of the orthocenter can be visually illustrated. Suitable for students at the junior high school level and above for geometric construction.

GeoGebra Commands & Parameters

  1. Segment(A, B) → a
  2. Segment(B, C) → b
  3. Segment(A, C) → c
  4. OrthogonalLine(A, b) → d
  5. OrthogonalLine(B, c) → e
  6. OrthogonalLine(C, a) → f
  7. Intersect(d, e) → D
  8. Intersect(e, c) → E
  9. Angle(D, E, C) → α
  10. Angle(d, b) → β
  11. Intersect(d, b) → F
  12. Angle(D, F, B) → γ
  13. Angle(D, F, B) → δ
  14. Intersect(f, b) → G
  15. Intersect(f, a) → H
  16. Angle(B, H, D) → ε

AI Drawing Prompt Reference

Draw a triangle and construct the altitudes from each vertex to the opposite side, marking the intersection point of these altitudes as the orthocenter. Then, measure and label the angles formed by the orthocenter, vertices, and feet of the altitudes to illustrate its geometric properties.
The prompt above was compiled from the original drawing commands and is for reference only.