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At a Glance

The area of a regular pentagon looks about twice as a big as the pentangle star drawn within it. Is it?

Golden Triangle

Three triangles ABC, CBD and ABD (where D is a point on AC) are all isosceles. Find all the angles. Prove that the ratio of AB to BC is equal to the golden ratio.

Darts and Kites

Explore the geometry of these dart and kite shapes!


Age 14 to 18
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 $BE$.