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Orthocenter, Circumcenter, and Centroid of Triangle

Orthocenter, Circumcenter, and Centroid of Triangle
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2018-11-13 01:08
TriangleVectorCoordinate Geometry
This example demonstrates the orthocenter, circumcenter, and centroid of a triangle. The orthocenter is the intersection of the three altitudes, the circumcenter is the intersection of the three perpendicular bisectors of the sides, and the centroid is the intersection of the three medians. Using GeoGebra commands such as Segment, Line, Midpoint, LineBisector, and Intersect, this example provides a visual understanding of these geometric concepts. Suitable for middle school and above students to learn about triangle geometry.

GeoGebra Commands & Parameters

  1. Segment(B, A) → f
  2. Segment(A, C) → g
  3. Segment(C, B) → h
  4. Line(B, A) → i
  5. Line(A, C) → j
  6. Line(B, C) → k
  7. Midpoint(A, B) → D
  8. Midpoint(A, C) → E
  9. Midpoint(C, B) → F
  10. Segment(D, E) → l
  11. Segment(E, F) → m
  12. Segment(F, D) → n
  13. Line(D, E) → p
  14. Line(D, F) → q
  15. Line(F, E) → r
  16. LineBisector(A, B) → s
  17. LineBisector(A, C) → t
  18. LineBisector(C, B) → a
  19. Intersect(s, t) → G
  20. OrthogonalLine(C, f) → b
  21. OrthogonalLine(A, k) → c
  22. OrthogonalLine(B, j) → d
  23. Intersect(b, c) → H
  24. Segment(B, E) → e
  25. Segment(C, D) → f_1
  26. Segment(A, F) → g_1
  27. Intersect(e, f_1) → I

AI Drawing Prompt Reference

Draw a triangle ABC, then draw its three medians, three perpendicular bisectors, and three altitudes. Find the intersection of the three medians, which is the centroid G; find the intersection of the three perpendicular bisectors, which is the circumcenter O; find the intersection of the three altitudes, which is the orthocenter H.
The prompt above was compiled from the original drawing commands and is for reference only.