Stage: 5 Challenge Level: 
 |
Show that the edges $AD$ and $BC$ of a tetrahedron $ABCD$ are mutually perpendicular when: $AB^2+CD^2 = AC^2+BD^2$. |
Geometric sequence. Vector algebra. Surds. Tetrahedra. Modulus arithmetic. Quadratic equations. Pythagoras' theorem. Long problems. Vector geometry. Vector notation.
Published June 1998.
Copyright © 2007. University of Cambridge. All rights reserved.
NRICH is part of the family of activities in the Millennium Mathematics Project, which also includes the Plus and Motivate sites.
email: nrich@damtp.cam.ac.uk
