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Medians Centroid Theorem (Proof without Words)

Medians Centroid Theorem (Proof without Words)
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2017-06-13 04:21
TriangleGeometric Construction
This example demonstrates the construction of medians and centroid in a triangle, providing a visual proof of the centroid theorem. Core concepts include medians, centroid, and geometric construction. It uses GeoGebra commands like Segment, Midpoint, Intersect, and Polygon. Suitable for high school students to understand the geometric properties of the centroid theorem.

GeoGebra Commands & Parameters

  1. Segment(A, B) → a_1
  2. Segment(B, C) → b_1
  3. Midpoint(a_1) → E_1
  4. Midpoint(b_1) → F_1
  5. Segment(C, E_1) → d_1
  6. Segment(A, F_1) → e_1
  7. Intersect(d_1, e_1) → G
  8. Segment(C, G) → c
  9. Segment(G, E_1) → d
  10. Segment(A, G) → a
  11. Segment(G, F_1) → b
  12. Segment(B, G) → e
  13. Midpoint(A, C) → E
  14. Midpoint(C, B) → D
  15. Midpoint(B, A) → F
  16. Segment(A, E) → c_1
  17. Segment(E, C) → f_1
  18. Segment(C, D) → l
  19. Segment(D, B) → m
  20. Segment(B, F) → n
  21. Segment(F, A) → p
  22. Segment(G, E) → f
  23. Segment(C, F) → g
  24. Segment(A, D) → h
  25. Segment(B, E) → i
  26. Midpoint(C, G) → H
  27. Midpoint(A, G) → I
  28. Midpoint(B, G) → J
  29. Segment(C, H) → k_1
  30. Segment(H, G) → l_1
  31. Segment(G, F) → m_1
  32. Segment(A, I) → n_1
  33. Segment(I, G) → p_1
  34. Segment(G, D) → q_1
  35. Segment(B, J) → r_1
  36. Segment(J, G) → s_1
  37. Segment(G, E) → t_1
  38. Polygon(A, B, C) → poly1, c_2, a_2, b_2