## Generalizing the concepts of perpendicular bisectors, angle bisectors, medians and altitudes of a triangle to 3D

A triangle is the most elementary, finite figure in the plane bounded by straight lines. Analogously, a tetrahedron is the most elementary solid in space bounded by planes.

Consider the corresponding *analogues* of the concepts of

1) perpendicular bisectors,

2) angle bisectors,

3) medians,

4) altitudes,

of a triangle for a tetrahedron, and investigate which of these are also concurrent for a tetrahedron.

**Challenge**: If true, prove it; if not, provide a counter-example.

First spend some time thinking about these, then click on each of the links above for a dynamic, interactive *Cabri 3D* applet to investigate the corresponding analogue in 3D.

Created by Michael de Villiers, 27 April 2012; updated 21 April 2024.