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Three Medians in a Triangle

Three Medians in a Triangle
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2014-01-24 13:59
TriangleGeometric Construction
In collections Median Triangle
This example explores the geometric relationship of the three medians in a triangle and how the centroid divides each median. It covers core concepts like medians, centroid, and segment division ratios. Constructed using commands such as Point, Polygon, Midpoint, Segment, and Intersect. Ideal for middle school and above to understand geometric properties and the role of the centroid.

GeoGebra Commands & Parameters

  1. Point(h) → B
  2. Point(g) → C
  3. Point(h) → A
  4. Polygon(A, B, C) → poly1, c, a, b
  5. Midpoint(a) → D
  6. Midpoint(b) → E
  7. Midpoint(c) → F
  8. Segment(C, F) → d
  9. Segment(A, D) → e
  10. Segment(B, E) → f
  11. Intersect(d, e) → G
  12. Segment(C, G) → i
  13. Segment(G, F) → j
  14. Segment(A, G) → k
  15. Segment(G, D) → l
  16. Segment(B, G) → m
  17. Segment(G, E) → n
  18. Polygon(D, C, G) → poly2, g_1, d_1, c_1
  19. Polygon(G, C, E) → poly3, e_1, g_2, c_2
  20. Polygon(G, E, A) → poly4, a_1, g_3, e_2
  21. Polygon(G, F, A) → poly5, a_2, g_4, f_1
  22. Polygon(G, D, B) → poly6, b_1, g_5, d_2
  23. Polygon(G, F, B) → poly7, b_2, g_6, f_2
  24. Segment(C, F) → q
  25. Segment(E, B) → r
  26. Segment(D, A) → s
  27. Intersect(q, r) → H

AI Drawing Prompt Reference

Draw a triangle and find the midpoint of each side. Connect each midpoint to the opposite vertex to form three medians. Observe that the three medians intersect at a point called the centroid, dividing each median into two segments with a 1:2 ratio, where the segment closer to the vertex is longer. Highlight the medians, centroid, and the divided segments with different colors or thicknesses to emphasize the relationships between the medians, vertices, and sides.
The prompt above was compiled from the original drawing commands and is for reference only.