Stage: 4 and 5 Challenge Level: 
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. Prove that triangles EFB and DFC are similar and hence show that the length EB is equal to the golden ratio and find the ratio BF : FD.
Rhombi. Mathematical reasoning & proof. Pentagons. Ratio. Golden ratio. Inequality/inequalities. Quadratic equations. Angle properties of shapes. Manipulating algebraic expressions/formulae. Similarity.
Published October 2001.
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