The straightedge allows us to construct lines and line segments, and the compass allows us to make circles with a specific radius. With these tools, we can reason about distances to explain why certain shapes have certain properties. For example, when we construct a regular hexagon using circles of the same radius, we know all the sides have the same length because all the circles are the same size. The hexagon is called inscribed because it fits inside the circle and every vertex of the hexagon is on the circle.

Similarly, we could use the same construction to make an inscribed triangle. If we connect every other point around the center circle, it forms an equilateral triangle. We can conjecture that this triangle has 3 congruent sides and 3 congruent angles because the entire construction seems to stay exactly the same whenever it is rotated of a full turn around the center.