Complete these steps with a straightedge and compass:

1. Draw a point and label it .
2. Draw a circle centered at point with a radius of length .
3. Mark a point on the circle and label it .
4. Draw another circle centered at point that goes through point .
5. Draw a line segment between points and .

Here is a hexagon with all congruent angles and all congruent sides (called a “regular hexagon”).

1. Draw a copy of the regular hexagon using only your pencil and no other tools. Trace your copy onto tracing paper. Try to fold it in half. What happened?
2. Here is a figure that shows the first few steps to constructing the regular hexagon. Use straightedge and compass moves to finish constructing the regular hexagon. Trace it onto tracing paper and confirm that when you fold it in half, the edges line up.

   

3. How do you know each of the sides of the shape is the same length? Show or explain your reasoning.