# Construct a pentagon/proof

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*I say the figure ABCDE is a regular pentagon.*

## Proof: Inscribed Pentagon

### P 01

Consider a regular decagon AD'BE'CA'DB'EC' inscribed in a circle O with radius AO. Set AO = r = 1.

• We may consider the inscribed decagon **given** without having a construction.

### P 02

A decagon has 10 vertices and a pentagon has 5 vertices, so **if** we can construct the first **then** we can construct the second.

### P 03

Connect every vertex of the decagon to every other vertex.

• This is called a *complete graph*.

### P 04

Remove most of the lines from the last figure, for simplicity. Find the intersection of DD' and A'E; call this N.

### P 05

Since the complete circle has an angle of 2π, the angle connecting adjacent vertices (such as