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In elementary geometry the word congruent is often used as follows. [2] The word equal is often used in place of congruent for these objects. Two line segments are congruent if they have the same length. Two angles are congruent if they have the same measure. Two circles are congruent if they have the same diameter.
I wouldn't say it is an alternative usage of the word congruent as in congruent numbers (modulus) and congruent transformation (congruent matrices). It is within the usage of Congruence (geometry) using the definition for an angle given by the Cambridge University Press (thesaurus.maths.org) - an angle is a measure of turn.
Any two pairs of angles are congruent, [4] which in Euclidean geometry implies that all three angles are congruent: [a] If ∠BAC is equal in measure to ∠B'A'C', and ∠ABC is equal in measure to ∠A'B'C', then this implies that ∠ACB is equal in measure to ∠A'C'B' and the triangles are similar. All the corresponding sides are ...
In mathematics, a congruent transformation (or congruence transformation) is: Another term for an isometry ; see congruence (geometry) . A transformation of the form A → P T AP , where A and P are square matrices, P is invertible , and P T denotes the transpose of P ; see Matrix Congruence and congruence in linear algebra .
The pons asinorum in Oliver Byrne's edition of the Elements [1]. In geometry, the theorem that the angles opposite the equal sides of an isosceles triangle are themselves equal is known as the pons asinorum (/ ˈ p ɒ n z ˌ æ s ɪ ˈ n ɔːr ə m / PONZ ass-ih-NOR-əm), Latin for "bridge of asses", or more descriptively as the isosceles triangle theorem.
For a given positive integer , two integers and are called congruent modulo , written a ≡ b ( mod n ) {\displaystyle a\equiv b{\pmod {n}}} if a − b {\displaystyle a-b} is divisible by n {\displaystyle n} (or equivalently if a {\displaystyle a} and b {\displaystyle b} have the same remainder when divided by n {\displaystyle n} ).
Congruent dissolution: substances dissolve congruently when the composition of the solid and the dissolved solute stoichiometrically match; Congruent melting occurs during melting of a compound when the composition of the liquid that forms is the same as the composition of the solid
The orange and green quadrilaterals are congruent; the blue one is not congruent to them. Congruence between the orange and green ones is established in that side BC corresponds to (in this case of congruence, equals in length) JK, CD corresponds to KL, DA corresponds to LI, and AB corresponds to IJ, while angle ∠C corresponds to (equals) angle ∠K, ∠D corresponds to ∠L, ∠A ...