How to Construct a Regular Pentagon

Reviewed by Joseph Meyer

Last Updated: December 24, 2021

A regular pentagon is a five-sided polygon with sides of equal length and interior angles of 108° (3π/5 rad). Because 5 is a Fermat prime, you can construct a regular pentagon using only a straightedge and compass.

Steps

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1
Draw a line segment AB.^{[1]
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2
Draw two circles, 1 and 2, centred at A and B, both with radius AB. The points where they intersect each other are C and D.^{[2]
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3
Connect C and D.
4
Draw circle 3 with centre C and radius AB. Circle 3 intersects circles 1 and 2 in E and F respectively. It also intersects line segment DC in G.^{[3]
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5
Connect E and F with G. Extend these lines far enough so they intersect circles 1 and 2. Call these new intersection points H and I.
6
Draw circles 4 and 5 centred at H and I with radius AB. Name the upper intersection point J.^{[4]
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7
Connect A, B, I, J and H.^{[5]
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8
Trace the pentagon in ink or another colour and erase any construction lines (if needed).

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Tips

Place a piece of cardboard or a book under your paper to prevent the compasses from slipping.

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Use a sharp pencil for increased precision.

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