Central symmetry is one of the key points in mathematics learning. Central symmetry figure refers to a figure in the same plane, if it is rotated 180 degrees around a certain point, and the rotated figure can completely coincide with the original figure, then this figure is called central symmetry figure. Common central symmetry figures include rectangle, square, circle, etc.
Is Rectangle Centrally Symmetric
A rectangle is an axisymmetric figure as well as a centrosymmetric figure.
Since the rectangle is folded in half along two long midpoint lines or two wide midpoint lines, the two sides of the polyline can be completely coincident. Therefore, the rectangle is an axisymmetric figure and has two symmetry axes.
Since the rectangle revolves around the intersection of two diagonal lines and the figure can be completely coincident with the original figure after rotating 180 °, the rectangle is also a centrally symmetric figure.
Tips for judging centrosymmetric figures
If a figure rotates 180 degrees around a certain point, and the rotated figure can completely coincide with the original figure, then this figure is called a centrosymmetric figure. And this central point is called the centrosymmetric point.
A simple method to determine that a figure is centrosymmetric: take the intersection of the horizontal and vertical vertical lines of the "cross" as the center of the figure, divide the figure into "cross" areas. If the shape of some figures in the diagonal area is identical and the distance from the corresponding point to the center is equal, the figure is centrosymmetric.
On the contrary, as long as there is a diagonal area with different shapes, the figure is not centrosymmetric. The "cross" distinguishing method is based on the definition of central symmetric figure. Because the "+" area of a figure divided by the symmetric center, some figures in the diagonal area must overlap after rotating 180 °, so this method has its scientific basis and specific operability.
Common centrosymmetric figures include rectangle, diamond, square, parallelogram, circle, and some irregular figures.
What is the difference between a central symmetric figure and an axial symmetric figure
1. Different properties: axial symmetry is about linear symmetry, and central symmetry is about point symmetry.
2. The theorems are different: axisymmetry is folding, involving the folding of space; Central symmetry is the positional relationship between two figures in a plane, and central symmetry figure is a figure with unique characteristics.
The connection between axial symmetry and central symmetry: central symmetry figures are not necessarily axial symmetry figures, and axial symmetry figures are not necessarily central symmetry figures. But a figure can be both axisymmetric and centrosymmetric, such as rectangle, circle, straight line, etc; Or neither, such as a triangle with unequal sides.