Stage: 4 and 5 Challenge Level: 
 |
$ABCDE$ is a regular pentagon of side length one unit. $BC$
produced meets $ED$ produced at $F$. Show that triangle $CDF$ is
congruent to triangle $EDB$.
Find the length of $BE$.
|
Congruence. Mathematical reasoning & proof. Quadratic equations. Fibonacci sequence. Pythagoras' theorem. Surds. Angle properties of shapes. Golden ratio. Pentagons. Long problems.
Published November 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