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What kinds of symmetries are there in mathematics?
There are three kinds, namely: axisymmetric figure, central symmetrical figure and rotational symmetrical figure.

Features:

Axisymmetric figure: When a figure is folded in half along a straight line, the two parts completely overlap.

Centrally symmetric figure: a figure rotates 180 degrees around a certain point, and the rotated figure can completely coincide with the original figure.

Rotationally symmetric figure: a figure rotates an angle around a fixed point and completely coincides with the original figure.

Extended data properties:

A straight line perpendicular to and bisecting a line segment is called the perpendicular bisector of the line segment, or the vertical centerline. The point on the vertical line in the line segment is equal to the distance between the two ends of the line segment.

In an axisymmetric figure, the corresponding points on both sides of the axis of symmetry are vertically bisected by the axis of symmetry. Two symmetrical figures are congruent. If two figures are symmetrical about a straight line, then the symmetry axis is the middle perpendicular of the line segment connected by any pair of corresponding points.

There are rectangles, diamonds, squares, parallelograms, circles, some irregular figures and so on.

Even-numbered polygons are centrosymmetric figures, odd-numbered polygons are not centrosymmetric figures, and regular triangles are axisymmetric figures, but not centrosymmetric figures. The isosceles trapezoid is not a centrally symmetric figure, but an axisymmetric figure.

Rotation angle is 0 degrees.