Point of Concurrency of Medians - Centroid

Point of Concurrency of Medians - Centroid
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2015-11-26 06:21
This example demonstrates that the medians of a triangle are concurrent at a single point known as the centroid. It involves core mathematical concepts like medians, concurrency, centroids, and triangle geometry. The construction uses commands such as Polygon, Midpoint, Line, Intersect, Segment, and Distance. It is suitable for middle school and above students studying triangle properties or as a geometric construction demonstration.

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. Line(A, F) → d
  6. Line(E, B) → e
  7. Line(C, D) → f
  8. Intersect(d, f) → G
  9. Segment(A, D) → g
  10. Segment(D, B) → h
  11. Segment(B, F) → i
  12. Segment(F, C) → j
  13. Segment(C, E) → k
  14. Segment(E, A) → l
  15. Distance(B, G) → distanceBG
  16. Distance(G, E) → distanceGE
  17. Distance(B, E) → distanceBE