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A hexagon need not have any lines of symmetry. Or, it can have just one line of symmetry. A regular hexagon has six lines of symmetry, including three along the lines bisecting the angles and three along the lines formed by bisecting the sides. A regular hexagon has a rotational order of 6.
Drawing circles, bisecting angles and creating perpendicular lines just to name a few
It can have.
You can tell if a ray is bisecting an angle if the angle is cut directly in half into two congruent parts.