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Triangle Parts: Midsegment, Median, Centroid

Triangle Parts: Midsegment, Median, Centroid
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2018-12-26 23:21
TrianglePolygonGeometric Construction
In collections Parts of a Triangle
This example demonstrates the geometric properties and relationships of the midsegment, median, and centroid in a triangle. Key math concepts include the midsegment theorem, median properties, centroid definition, and its coordinate formula. GeoGebra commands/objects used in construction are Polygon, Midpoint, Segment, Distance, Intersect, and Angle. Suitable for high school geometry teaching or self-exploration.

GeoGebra Commands & Parameters

  1. Polygon(A, B, C) → t1, c, a, b
  2. Midpoint(A, B) → D
  3. Midpoint(B, C) → E
  4. Midpoint(A, C) → F
  5. Segment(F, E) → f
  6. Segment(E, D) → g
  7. Segment(D, F) → h
  8. Distance(B, A) → distanceBA
  9. Distance(E, F) → distanceEF
  10. Polygon(N, O, P) → t3, p_1, n_1, o
  11. Midpoint(P, O) → Q
  12. Segment(N, Q) → t
  13. Distance(Q, O) → distanceQO
  14. Distance(Q, P) → distanceQP
  15. Polygon(G, H, I) → t2, i, g_1, h_1
  16. Midpoint(H, G) → J
  17. Midpoint(G, I) → K
  18. Midpoint(I, H) → L
  19. Segment(H, K) → j
  20. Segment(I, J) → k
  21. Segment(G, L) → l
  22. Intersect(j, k) → M
  23. Distance(H, M) → distanceHM
  24. Distance(M, K) → distanceMK
  25. Angle(F, A, B) → α
  26. Angle(C, F, E) → β
  27. Segment(B, E) → m
  28. Segment(E, C) → n
  29. Segment(F, A) → p
  30. Segment(F, C) → q
  31. Segment(A, B) → r
  32. Segment(Q, O) → s
  33. Segment(Q, P) → d
  34. Segment(P, N) → e
  35. Segment(N, O) → f_1
  36. Segment(J, G) → i_1
  37. Segment(J, H) → j_1
  38. Segment(H, L) → k_1
  39. Segment(L, I) → l_1
  40. Segment(I, K) → m_1
  41. Segment(K, G) → q_1