Some regular polygons have an even number of sides. Other regular polygons have an odd number of sides. How does the number of sides, even or odd, affect the position of the line of reflection for mapping the polygon onto itself? Explain.

Answer: When a line of reflection coincides with a line of symmetry, the polygon maps onto itself. The position of the line of symmetry depends on the number of sides. For regular polygons with an even number of sides, lines of symmetry are the perpendicular bisectors of the opposite sides and the angle bisectors of opposite vertices. However, the symmetry of regular polygons with an odd number of sides does not allow lines of symmetry to connect the opposite pairs of vertices, so they have symmetry only along the perpendicular bisectors.

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