# How to Construct a Regular Heptagon

15-03-2017, 21:20
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A regular heptagon (also called septagon) is a polygon with seven equal sides and seven equal angles. Accurately constructing polygons is an important part of geometry, and for regular heptagons there are multiple ways to draw one. Here is the easiest method, using a straight edge and compass.

### Steps

1. Draw an arbitrary circle, centred at a point X{\displaystyle X}. Keep in mind that you will need some extra space around the circle for construction lines.
2. Draw the radius AX{\displaystyle AX}.
3. Draw a circle with radius AX{\displaystyle AX}, centred at A{\displaystyle A}. This circle intersects the first circle at points B{\displaystyle B} and C{\displaystyle C}.
4. Connect B{\displaystyle B} and C{\displaystyle C}. BC{\displaystyle BC} bisects AX{\displaystyle AX} in E{\displaystyle E}.
5. Draw a third circle with radius BE{\displaystyle BE}, centred at B{\displaystyle B}. This circle intersects circle a in D{\displaystyle D}.
6. Connect B{\displaystyle B} and D{\displaystyle D}. BD{\displaystyle BD} is one side of the regular heptagon.
7. Use your compass to trace the distance BD around the circle. You should end up exactly where you started.
9. Erase the construction lines if needed.

## Tips

• Put a piece of cardboard or a book under your paper so your compass doesn't slip.
• Sharpen your pencils before beginning, for increased accuracy.

## Things You'll Need

• Paper
• Compass
• Straight edge
• Pencil
• Pen
• Eraser
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