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Centroid of a Tetrahedron: Medians and Bimedians

Centroid of a Tetrahedron: Medians and Bimedians
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2014-10-06 05:16
VectorSolid GeometryGeometric Construction
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This example demonstrates the geometric properties of medians and bimedians in a tetrahedron. Key math concepts include the centroid, medians, bimedians, midpoints, line segments, and similarity transformations. Construction involves commands like Polygon, Pyramid, Midpoint, Segment, Dilate, and Intersect to build the tetrahedron and its medians and bimedians. Suitable for high school students and educators.

GeoGebra Commands & Parameters

  1. Polygon(A, B, C) → poly1, c, a, b
  2. Pyramid(poly1, D) → d, faceABD, faceBCD, faceACD, edgeAD, edgeBD, edgeCD
  3. Midpoint(edgeBD) → E
  4. Midpoint(c) → F
  5. Midpoint(edgeAD) → G
  6. Midpoint(b) → H
  7. Midpoint(edgeCD) → I
  8. Midpoint(a) → J
  9. Segment(E, H) → e
  10. Segment(G, J) → f
  11. Segment(I, F) → g
  12. Dilate(B, 0.3333333333333333, I) → B'
  13. Dilate(C, 0.3333333333333333, G) → C'
  14. Dilate(A, 0.3333333333333333, E) → A'
  15. Dilate(C, 0.3333333333333333, F) → C'_1
  16. Segment(D, C'_1) → h
  17. Segment(B, C') → i
  18. Segment(A, B') → j
  19. Segment(C, A') → k
  20. Intersect(j, k) → K