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 perpendicular edge bisector in space is the analogue of a perpendicular bisector in the plane. Hence, a perpendicular edge bisector is the set of points equidistant from two vertices, or equivalently, it is the plane that perpendicularly bisects the edge connecting two vertices. Click perpendicular edge bisector demo to view a Cabri 3D applet that illustrates this concept, and that you can manipulate.
Theorem 1: The six perpendicular edge bisectors of a tetrahedron are concurrent (at the circumcentre of the tetrahedron, and therefore the tetrahedron has a circumsphere).
Challenge: Can you explain (prove) why this theorem is true? (Hint: use the idea of equi-distance.) 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 21 April 2024.