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Since a regular hexagon contains no circles, it can be drawn using only a straightedge.

Question

Since a regular hexagon contains no circles, it can be drawn using only a straightedge.

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Solution 1

This statement is partially correct. A regular hexagon can indeed be drawn using only a straightedge, but it doesn't have anything to do with the fact that it contains no circles. The ability to draw a shape using only a straightedge depends on the angles and lines that make up the shape, not whether it contains a circle or not.

Here are the steps to draw a regular hexagon using only a straightedge:

  1. Draw a straight line. This will be one side of your hexagon.
  2. Use your straightedge to draw another line at an angle of 120 degrees from the first line. This will be the second side of your hexagon.
  3. Repeat this process to draw the remaining four sides of the hexagon. Each side should be the same length and each angle should be 120 degrees.
  4. Once you have drawn all six sides, you should have a regular hexagon.

Remember, a regular hexagon is a six-sided polygon where all sides are of equal length and all internal angles are of equal measure (120 degrees).

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Solution 2

This statement is partially correct. A regular hexagon can indeed be drawn using only a straightedge, but not because it contains no circles. The reason is that a regular hexagon can be constructed using only straight lines. However, the process of constructing a regular hexagon with a straightedge alone is not straightforward and requires knowledge of geometry. Here are the steps:

  1. Draw a straight line of any length. This will be one side of the hexagon.
  2. Using the straightedge, extend a line from each end of the first line at an angle of 120 degrees. These will be the next two sides of the hexagon.
  3. Extend two more lines from the ends of these lines, again at an angle of 120 degrees. These will be the final two sides of the hexagon.
  4. Adjust the lengths of the lines as necessary to ensure that all six sides are of equal length.

This method assumes that you can measure angles with the straightedge, which is not typically possible. Therefore, while it is theoretically possible to draw a regular hexagon with a straightedge alone, in practice it would be very difficult without additional tools.

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