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Euler Line of a Triangle by heinos

Euler Line of a Triangle by heinos
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2014-11-18 03:14
TriangleCoordinate GeometryGeometric Construction
This example demonstrates the Euler line of a triangle, which contains the orthocenter, centroid, and circumcenter. By constructing these special points, you can observe that they are collinear. Commands used include Polygon, Midpoint, Segment, OrthogonalLine, Intersect, and Line. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. Polygon(A, B, C) → poly1, c, a, b
  2. Midpoint(c) → D
  3. Midpoint(b) → E
  4. Midpoint(a) → F
  5. Segment(A, F) → d
  6. Segment(B, E) → e
  7. Segment(C, D) → f
  8. OrthogonalLine(F, a) → g
  9. OrthogonalLine(E, b) → h
  10. OrthogonalLine(D, c) → i
  11. Intersect(i, g) → Circumcenter
  12. Segment(B, E) → j
  13. Segment(F, A) → k
  14. Segment(C, D) → l
  15. Intersect(l, k) → Centroid
  16. Line(A, B) → m
  17. Line(A, C) → n
  18. Line(C, B) → p
  19. OrthogonalLine(C, m) → q
  20. OrthogonalLine(A, p) → r
  21. OrthogonalLine(B, n) → s
  22. Intersect(q, s) → Orthcenter
  23. Line(Circumcenter, Centroid) → t

AI Drawing Prompt Reference

Draw a triangle and find its centroid, orthocenter, and circumcenter, which are collinear. First, draw the triangle's three sides, then construct the perpendicular bisectors of each side to locate the orthocenter and circumcenter. Next, find the centroid of the triangle, and finally connect the circumcenter and centroid with a line to demonstrate their collinearity.
The prompt above was compiled from the original drawing commands and is for reference only.