We explain what congruence is and its differences from coherence. Furthermore, its meaning in geometry and law.
What is congruence?
We speak of congruence to refer to something that has a certain logical relationship with its environment or with another specific referencein a similar way to what is expressed by the nouns convenience and coherence, of which it is often used as a synonym.
The word congruence comes from Latin congruentword formed by the voices with (“next to”) and grumble (“coincidir”), although this etymology is somewhat uncertain, since the verb grumble Only records are preserved that associate it with “screaming like a crane” or “imitating the sound of a crane”, which does not seem to make much sense in this context.
In any case, The exact concept of congruence is usually determined by the context in which it is used. For example, in law we speak of congruence when there is agreement between the court's ruling and the claims of the parties involved in the litigation.
But the meaning of the word changes in the field of religion, on the other hand, where it expresses God's ability to act without contravening the free will of human beings, and so on in other areas of knowledge.
Congruence and coherence
Although they are often used as synonyms, these two terms – coherence and congruence – do not have the exact same meaning in all contexts. Both express a logical relationship between two referentsbut they differ in a more or less subtle aspect: coherence implies a logical relationship of conformity, while congruence implies a logical relationship of convenience.
This means that something coherent is something that follows the same logicwhich is part of the same way of thinking or which appears unified, consistent with itself. For example, it is consistent for a politician with a conservative affiliation to vote against the changes proposed by the progressive sectors. It is coherent because its theory (its ideology) and its practice (its political decisions) are consistent.
Instead, something is congruent when it agrees with your desires, conveniences or aspirations.
In the same example, if the politician with a conservative affiliation has many aspirations to be elected president, it would be consistent for him to vote in favor of the changes coming from the progressive sectors, that is, from his rivals, if this translates into better and clearer opportunities to have the necessary support to rise to power. His aspirations (being elected) and his actions (gaining support in unexpected sectors) are consistent.
Congruence in geometry
In mathematics, specifically in the branch of geometry, the term congruence is used to designate the relationship between two geometric figures that have the same dimensions and the same shaperegardless of their spatial orientation, rotation or reflection, that is, when an isometric relationship exists between them.
Thus, as far as Euclidean geometry is concerned, congruence refers to the arithmetic and algebraic equivalence of mathematical expressions of two figures. While in analytical geometry it requires that the Euclidean distance between any pair of points of a figure in a Cartesian coordinate system be equal to those of a second figure.
For example, two angles are congruent when a 180° rotation about their vertex makes them coincide exactly with each other.
Congruence and similarity of triangles
Two triangles are congruent when they have an isometric relationship with each other, which is expressed mathematically as follows: 🔺ABC≅🔺DEF (that is: triangle ABC is congruent with triangle DEF). This can occur in any of the following cases:
- AAL or ALA case. Two triangles are congruent when they have two equal angles and the side between them, since by knowing two of the angles of a triangle, we can determine the third.
ALA case
AAL case
- LAL case. Two triangles are congruent if they have the same two given sides and the angle where they touch.
- LLL case. Two triangles are congruent if they have three equal sides.
- LLA case. Two triangles are congruent if they have two equal sides and the angle opposite that of said sides is also equal. But we must know if it is a right triangle or if its angles are obtuse, first.
Congruence principle
In procedural law, the principle of congruence is known as a maxim that requires the judge of any litigation to reach conclusions that are congruent, that is, consistent, with the requests of the parties in the lawsuit and with the facts recorded in the case. the same.
This means that a judge must make a decision within the framework of the aspirations of the parties in disputewithout involving causes unrelated to the case in question and without exceeding the compensation requested by the plaintiff. This means that the judge must operate within the parameters dictated by the case itself.
However, depending on the legal framework of each country, there are specific matters in which the principle of congruence may present exceptions, such as family matters or when it is necessary to provide special protection to one of the parties.
Continue with: Harmony
References
- “Congruence (number theory)” on Wikipedia.
- “Congruence (geometry)” on Wikipedia.
- “Congruence” in the Language Dictionary of the Royal Spanish Academy.
- “Radication of Congruence” in the Online Spanish Etymological Dictionary.
