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The diagram shows a regular pentagon with sides of unit length. Find all the angles in the diagram. Prove that the quadrilateral shown in red is a rhombus.

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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.

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Golden Mathematics

A voyage of discovery through a sequence of challenges exploring properties of the Golden Ratio and Fibonacci numbers.


Stage: 5 Challenge Level: Challenge Level:1
There are four cases to consider:
(a) the group containing only the identity transformation
(b) groups containing the identity and rotations
(c) groups containing the identity and reflections
(d) groups containing the identity, reflections and rotations.