In mathematics, the congruence of two geometric figures is formed when the two have the same dimensions and the same shape regardless of their position or orientation. They are two congruent figures and they are if there is an isometry that links them, a conversion that can be translation, rotation and reflection.
Linked parties are known as homologous or corresponding. After making the isometry and when superimposing the figures, all the points must agree. In order for the figures to be congruent, they must have the following requirements:
- All of its corresponding interior angles must be equal.
- All corresponding sides must have the same measure.
In the area of triangles, it is not necessary to prove the congruence of the 6 pairs of elements (3 pairs of sides and 3 pairs of angles), some conditions can be verified with the congruence of three pairs of elements and they are the following:
- Two triangles are congruent if all three of their sides are equal.
- Two triangles are congruent two of their sides are equal and the angle between them is understood.
- Two triangles are congruent if they have a suitable side and the angles with a vertex at each endpoint of that side are congruent.
- Two triangles are congruent if they have two suitable sides and the angles opposite the larger side are also congruent.
In mathematics, two similar or similar geometric figures are considered if they have the same shape regardless of the size they represent.
The convenient sides must be equal according to a similarity ratio, scale factor or constant of proportionality. The similarity ratio is acquired when the measurement of one side is divided by its corresponding one, the number reached must be constant for all the sides of the figure.
For two figures to be similar they have to fulfill the following:
- Their corresponding (homologous) angles must be equal.
- Their corresponding sides are equal.
Their corresponding angles have to be equal. Its proper sides are equal. In the case of triangles, the shape varies according to their angles, so the notion of similarity is based on: Two triangles are similar if their angles are equal two to two.
To indicate that two triangles ABC and DEF are similar, write ABC ~ DEF, the order indicates the correspondence between the angles, that is, A, B and C that go with D, E and F, in order.
Difference Between Congruence and Similarity
- In triangles, congruence occurs when two triangles are equal, measure the same, and have the same angles regardless of their orientation.
- Two geometric figures are adequate if they both have the same dimensions and the same shape regardless of their position or orientation.
- The similarity in triangles occurs when, without being equivalent, they keep a proportion or scale in their sides and angles.
- Two geometric figures are similar if they have the same shape regardless of their size.