How to Construct a Regular Pentagon

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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.

Steps

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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]
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  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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      References

      1. ↑ https://demonstrations.wolfram.com/ConstructingARegularPentagonWithRulerAndCompass/
      2. ↑ https://www.youtube.com/watch?v=9vuJ3W0uD_8
      3. ↑ http://www.props.eric-hart.com/how-to/how-to-draw-a-pentagon-with-a-compass/
      4. ↑ http://www.props.eric-hart.com/how-to/how-to-draw-a-pentagon-with-a-compass/
      5. ↑ https://www.youtube.com/watch?v=I2GbLOzhMng

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