This dynamic 3D applet does not work on Internet Explorer, and works best on a relatively new version of the free browser Firefox - click link to download latest version. It also requires the downloading & installation of the free Cabri 3D Plug In, available at Windows (4 Mb) or Mac OS (13.4 Mb).
Basic manipulation: 1) Right click (or Ctrl + click) and drag to rotate the whole figure (glassball).
2) Click to select and hold down the left button to drag any of the vertices A, C or D of the tetrahedron.
Or click Summary of manipulation to open & resize a separate window with instructions.
The median of a tetrahedron is the analogue of a median of a triangle in the plane. Hence, since a median of a triangle connects a vertex with the centroid of an opposite side, a median of a tetrahedron is the line connecting a vertex with the centroid of an opposite face.
Theorem 3: The four medians of a tetrahedron are concurrent at its centroid (or centre of mass). More-over, the centroid divides each median in the ratio 3:1.
Challenge: Can you explain (prove) why this theorem is true? (Hint: use vectors.) Only if stuck, go to 3D Concurrency Proofs.
HTML export by Cabri 3D. Download a 30 day Demo, or for more information about purchasing this software, go to Cabri 3D.
Created by Michael de Villiers, 27 April 2012; updated 20 April 2024.