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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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1Draw a line segment AB.[1]
2Draw 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]Advertisement
3Connect C and D.
4Draw 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]
5Connect 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.
6Draw circles 4 and 5 centred at H and I with radius AB. Name the upper intersection point J.[4]
7Connect A, B, I, J and H.[5]
8Trace the pentagon in ink or another colour and erase any construction lines (if needed).
Expert Q&A
Tips
- Place a piece of cardboard or a book under your paper to prevent the compasses from slipping.Thanks
- Use a sharp pencil for increased precision.Thanks
References
- ↑ https://demonstrations.wolfram.com/ConstructingARegularPentagonWithRulerAndCompass/
- ↑ https://www.youtube.com/watch?v=9vuJ3W0uD_8
- ↑ http://www.props.eric-hart.com/how-to/how-to-draw-a-pentagon-with-a-compass/
- ↑ http://www.props.eric-hart.com/how-to/how-to-draw-a-pentagon-with-a-compass/
- ↑ https://www.youtube.com/watch?v=I2GbLOzhMng
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