# Centre of Symmetry of a Geometric Figure

## Centre of Symmetry of a Geometric Figure

Point in relation to which all the points in the figure are symmetric in pairs.

Therefore, the centre of symmetry of a figure is the centre of a point symmetry that overlays the figure onto itself.

### Examples

• Each endpoint of a segment whose endpoints are on the edge of the polygon and that passes through the centre O of the regular polygon is equidistant from point O. Therefore, the centre O is the centre of symmetry of the figure.

A regular hexagon has a centre of symmetry, but a regular pentagon does not have a centre of symmetry.
• The meeting point of the diagonal lines of a parallelogram is the centre of symmetry of the parallelogram. In this figure, points A and C are symmetric in relation to the centre E:

• The centre of a sphere is also its centre of symmetry.

• An isosceles trapezoid does not have a centre of symmetry unless it is a rectangle. Points A and C are not symmetric with respect to the intersection point E of its diagonals: