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