Definition of

# central symmetry

It is called **symmetry** to the **correspondence** that is registered between the position, the form and the size of those components that form a whole. **Central**for its part, is the adjective that refers to what is linked to a **center** (the space equidistant from the limits of something).

The **core symmetry**in this way, it is considered from a **spot** It is known as **center of symmetry**. All corresponding points in a central symmetry are called homologous points and allow you to draw homologous segments that are equal and have corresponding angles that also measure the same.

In other words, the points *TO* and *TO’* They are symmetric about a center of symmetry. *S* when *SA = SA’*being *TO* and *TO’* equidistant from *S*. It is important to note that *SA* and *SA’* have the same length.

Just as, in a central symmetry, the **image** of a segment is another segment with the same length, the image of a polygon is another polygon congruent to the original, while the image of a triangle is another congruent triangle.

This means, therefore, that we can say that in order to be effective, central symmetry must be based on two basic principles:

-That both the point and the center of symmetry and the so-called image belong to the same line.

-That the image and the point are at the same distance from a point, which is what is called the center of symmetry and which is the point where the two axes intersect.

If we focus on the **triangles**in those that are symmetric with respect to a point, it is possible to modify the **sign** of the coordinates to pass from any point to its symmetric.

Thus, if the coordinates of the points are *A = (5, 2)*, *B = (2, 4)* and *C = (4, -2)*the coordinates of its mirrors will be *A = (-5, -2)*, *B = (-2, -4)* and *C = (-4, 2)*.

When talking about central symmetry, it is usual that, in the same way, other types of symmetries are also put on the table as a way of comparing them and making clear the differences between them. Thus, for example, reference is often made to what is known as axial, cylindrical or radial symmetry.

Specifically, that is used to refer to the symmetry that is established around an axis. That is to say, it becomes clear at the moment that the points of a certain figure coincide with the points of another when a line is taken as a reference, which is the axis of symmetry.

It is also determined that one of the singularities of axial symmetry is that in it a line can cause the figures to be divided into two others that are congruent. However, the result of this can give rise to what are two inverse congruent forms, which are the ones that coincide by superposition at the moment in which they are rotated around what is the axis.