# Answer to Question #236 in Geometry for ken moore

Question #236

Prove that if a polygon has several axes of symmetry, they all intersect in one point.

Expert's answer

Place a single mass in every vertex of a polygon. Symmetry about the axis of symmetry moves this system of points into itself, so its center of mass also moves into itself. Consequently, all of the symmetry axes pass through the center of mass.

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