# Golden Pentagon

*By toni On 22 August, 2020 · Leave a Comment*

Find all the angles in the diagram and mark each set of equal angles in a colour for that set.

Let AE = 1 unit and BE = *x* units.

Which triangles are isosceles?

Which triangles are similar?

Use similar triangles to give an equation for* x *and solve the equation.

In each of these diagrams of a regular pentagon find the ratio of the length shown in red to the length in blue in terms of the Golden Ratio $\phi = \frac{1}{2}(1 + \sqrt 5)$.

Prove (1) $\frac{BE}{AE}=\phi$. (2) $\frac{BE}{BR}=\phi$. (3) $\frac{AE}{AR}=\phi$. (4) $\frac{AP}{PR}=\phi$.

Click here for the GOLDEN PENTAGON worksheet.

Click here for the GOLDEN PENTAGON Inclusion and Home Learning Guide.

Click here for the GOLDEN PENTAGON Notes for Teachers.

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