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Orthocenter Construction by hasulkin2

Orthocenter Construction by hasulkin2
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2014-10-01 09:56
TriangleCoordinate GeometryGeometric Construction
This example demonstrates how to find the orthocenter of a triangle step by step. The orthocenter is the point where the three altitudes of a triangle intersect. GeoGebra commands used include Segment, OrthogonalLine, Intersect, and Angle. Suitable for students learning coordinate geometry in middle school and above.

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 ABC. Then, construct a perpendicular line from point A to line BC, a perpendicular line from point B to line AC, and a perpendicular line from point C to line AB. The intersection of these three perpendicular lines is the orthocenter of triangle ABC.
The prompt above was compiled from the original drawing commands and is for reference only.