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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 number, you tin construct a regular pentagon using just a straightedge and compass.

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  1. one

    Draw a line segment AB. [i]

  2. two

    Describe two circles, 1 and ii, 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. iii

    Connect C and D.

  4. iv

    Draw circle three with centre C and radius AB. Circumvolve 3 intersects circles one and 2 in E and F respectively. Information technology likewise intersects line segment DC in G.[3]

  5. 5

    Connect East and F with Grand. Extend these lines far plenty so they intersect circles 1 and 2. Call these new intersection points H and I.

  6. 6

    Draw circles 4 and v centred at H and I with radius AB. Proper noun the upper intersection point J.[iv]

  7. 7

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

  8. 8

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

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

  • Utilise a sharp pencil for increased precision.

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