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Centroids & Orthocenters in Triangles

Centroids & Orthocenters in Triangles
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2015-12-22 23:29
TriangleCoordinate GeometryGeometric Construction
This example demonstrates the geometric properties and relationships of centroids and orthocenters in triangles. Key math concepts include centroid, orthocenter, midpoint, segment, intersection, and perpendicular line. Constructed using GeoGebra commands like Polygon, Midpoint, Segment, Intersect, and OrthogonalLine. Suitable for high school mathematics teaching or student exploration of geometric properties.

GeoGebra Commands & Parameters

  1. Polygon(A, B, C) → poly1, c, a, b
  2. Midpoint(A, B) → D
  3. Midpoint(B, C) → E
  4. Midpoint(C, A) → F
  5. Segment(D, C) → d
  6. Segment(A, E) → e
  7. Segment(B, F) → f
  8. Intersect(e, f) → G
  9. Polygon(H, I, J) → poly2, j, h, i
  10. OrthogonalLine(H, h) → g
  11. OrthogonalLine(J, j) → k
  12. OrthogonalLine(I, i) → l
  13. Intersect(k, g) → K