Central symmetry is a kind of correspondence.
Central symmetry is a type of correspondence that is considered from a point known as the center of symmetry . All corresponding points in a central symmetry are called homologous points and allow us to draw homologous segments that are equal and have corresponding angles that also measure the same.
It should be noted that symmetry is the correspondence that is recorded between the position, shape and 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).
About central symmetry
Regarding central symmetry, it can be said that the points A and A' are symmetrical with respect to a center of symmetry S when SA = SA' , with A and A' being 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 with the original, while the image of a triangle is another congruent triangle.
This means, therefore, that central symmetry to be effective 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 another point, which is called the center of symmetry and where the two axes intersect.
Central symmetry can occur in triangles.
Its application in triangles
If we focus on triangles , those that are symmetrical with respect to a point, it is possible to modify the sign of the coordinates to go from any point to its symmetrical one.
Thus, if the coordinates of the points are A = (5, 2) , B = (2, 4) and C = (4, -2) , the coordinates of their symmetry will be A = (-5, -2 ) , B = (-2, -4) and C = (-4, 2) .
Central symmetry and axial symmetry
When talking about central symmetry, it is common 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, it is common to refer to what is known as axial, cylindrical or radial symmetry.
Specifically, this notion is used to refer to the symmetry that is established around an axis. That is, it becomes clear at the moment that the points of a given figure coincide with the points of another when taken as reference to a line that is the axis of symmetry .
It is also determined that one of the singularities of axial symmetry is that a straight line can cause the figures to divide into two others that are congruent. However, the result of this can give rise to what are two inverse congruent shapes, which are those that coincide by superposition at the moment in which they are rotated around the axis.