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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.

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  1. 1

    Draw a line segment AB. [1]

  2. 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]

  3. 3

    Connect C and D.

  4. 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]

  5. 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. 6

    Draw circles 4 and 5 centred at H and I with radius AB. Name the upper intersection point J.[4]

  7. 7

    Connect A, B, I, J and H. [5]

  8. 8

    Trace the pentagon in ink or another colour and erase any construction lines (if needed).

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

  • Use a sharp pencil for increased precision.

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