Is an equilateral triangle a centrosymmetric figure?

Is an equilateral triangle a centrosymmetric figure?

No, according to the definition, only when rotated 180 degrees, the overlapped figure is centrosymmetric
The equilateral triangles do not coincide after 180 ° rotation

Proof: equilateral triangle is not a centrosymmetric figure

As shown in the figure, make an equilateral triangle BC, the height on the edge of AC intersects at point O, O is the center of the circumscribed circle of △ ABC, Ao = Bo = Co △ ABC rotates 120 ° around point O, the rotated figure can coincide with the original figure, and the centrosymmetric figure rotates a figure 180 ° around a certain point. If the rotated figure can coincide with the original figure, then the figure is called centrosymmetric figure So an equilateral triangle is not a centrosymmetric figure

An equilateral triangle is both a centrosymmetric figure and an axisymmetric figure with three axes of symmetry

In the plane, a figure rotates 180 ° around a point. If the figures before and after rotation can coincide with each other, then the figure is called a centrosymmetric figure, so the first conclusion is correct
An equilateral triangle is an equilateral triangle. An equilateral polygon has n axes of symmetry
So this sentence is right

The following statements are correct ()
A. If a line segment is rotated 180 ° around its midpoint and coincides with the original line segment, then the line segment is a centrosymmetric figure B. If an equilateral triangle is rotated 120 ° around the intersection of its three midlines and coincides with the original figure, then the equilateral triangle is a centrosymmetric figure C. If a square is rotated 90 ° around its diagonal intersection and coincides with the original figure, then the square is a centrosymmetric figure D If a pentagram rotates 72 ° around its center and coincides with the original figure, the pentagram is a centrosymmetric figure

A. If a line segment is rotated 180 ° around its midpoint and coincides with the original line segment, then the line segment is a centrosymmetric figure, so this option is correct; B. If an equilateral triangle is rotated 180 ° around the intersection of its three midlines and does not coincide with the original figure, then the equilateral triangle is not a centrosymmetric figure, so this option is wrong; C. It does not conform to the definition of centrosymmetric figure, and the square is around its diagonal If the intersection is rotated 180 ° and coincides with the original figure, then the square is a centrosymmetric figure, so this option is wrong; if D, the pentagram is rotated 180 ° around its center and does not coincide with the original figure, then the pentagram is not a centrosymmetric figure, so this option is wrong