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Construct the Orthocenter of a Triangle by Emily Crum

Construct the Orthocenter of a Triangle by Emily Crum
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2017-02-26 07:58
TriangleCoordinate GeometryGeometric Construction
This example demonstrates how to construct the orthocenter of a triangle. The orthocenter is the point where the three altitudes of a triangle intersect. By constructing the three vertices A, B, and C of the triangle, and then constructing the altitudes f, g, and h corresponding to these vertices, the intersection point D of these altitudes is the orthocenter. Commands used include Segment, Point, OrthogonalLine, and Intersect. Suitable for students at the junior high school level and above for geometric construction.

GeoGebra Commands & Parameters

  1. Segment(A, B) → f
  2. Segment(B, C) → g
  3. Segment(C, A) → h
  4. Point(f) → D
  5. Point(h) → E
  6. Point(g) → F
  7. Segment(D, E) → i
  8. Segment(E, F) → j
  9. Segment(F, D) → k
  10. OrthogonalLine(D, j) → l
  11. OrthogonalLine(F, i) → m
  12. OrthogonalLine(E, k) → n
  13. Intersect(l, m) → G

AI Drawing Prompt Reference

Draw a triangle ABC, then construct the altitudes f, g, and h from points A, B, and C respectively. The intersection point D of these altitudes is the orthocenter. Next, form triangle DEF by connecting points D, E, and F. Then, construct the perpendicular lines l to DE, m to EF, and n to FD. The intersection point G of lines l and m is another significant point related to the orthocenter.
The prompt above was compiled from the original drawing commands and is for reference only.