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# Pent

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### Golden Thoughts

### At a Glance

Links to the University of Cambridge website
Links to the NRICH website Home page

Nurturing young mathematicians: teacher webinars

30 April (Primary), 1 May (Secondary)

30 April (Primary), 1 May (Secondary)

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Age 14 to 18

Challenge Level

- Problem
- Student Solutions

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.

Rectangle PQRS has X and Y on the edges. Triangles PQY, YRX and XSP have equal areas. Prove X and Y divide the sides of PQRS in the golden ratio.

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