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Orthocenter of a Triangle by HGrega

Orthocenter of a Triangle by HGrega
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2016-01-29 23:14
TriangleCoordinate GeometryGeometric Construction
This example demonstrates the orthocenter of a triangle, which is the point where the three altitudes of a triangle intersect. Using GeoGebra commands such as Polygon, Line, OrthogonalLine, Intersect, and Angle, one can construct a triangle and find its orthocenter. Suitable for middle school and above students to learn triangle geometry.

GeoGebra Commands & Parameters

  1. Polygon(A, B, C) → poly1, c, a, b
  2. Line(A, C) → d
  3. Line(C, B) → e
  4. Line(B, A) → f
  5. OrthogonalLine(B, b) → g
  6. Intersect(d, g) → D
  7. Angle(B, D, C) → α
  8. OrthogonalLine(A, a) → h
  9. Intersect(e, h) → E_1
  10. OrthogonalLine(C, c) → i
  11. Intersect(f, i) → F
  12. Intersect(g, h) → E

AI Drawing Prompt Reference

Draw a triangle and construct the altitudes from each vertex to the opposite side. The intersection point of the three altitudes is the orthocenter of the triangle. First, draw the sides of the triangle, then draw the perpendicular lines from each vertex to the opposite side, and finally find the intersection point of the three perpendiculars, which is the orthocenter.
The prompt above was compiled from the original drawing commands and is for reference only.