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2. Congruence (geometry) - Wikipedia

   en.wikipedia.org/wiki/Congruence_(geometry)

   Definition of congruence in analytic geometry. In a Euclidean system, congruence is fundamental; it is the counterpart of equality for numbers. In analytic geometry, congruence may be defined intuitively thus: two mappings of figures onto one Cartesian coordinate system are congruent if and only if, for any two points in the first mapping, the ...

3. Congruence relation - Wikipedia

   en.wikipedia.org/wiki/Congruence_relation

   Particular definitions of congruence can be made for groups, rings, vector spaces, modules, semigroups, lattices, and so forth. The common theme is that a congruence is an equivalence relation on an algebraic object that is compatible with the algebraic structure, in the sense that the operations are well-defined on the equivalence classes .

4. Congruent number - Wikipedia

   en.wikipedia.org/wiki/Congruent_number

   In number theory, a congruent number is a positive integer that is the area of a right triangle with three rational number sides. [1][2] A more general definition includes all positive rational numbers with this property. [3] The sequence of (integer) congruent numbers starts with. For example, 5 is a congruent number because it is the area of ...

5. Congruum - Wikipedia

   en.wikipedia.org/wiki/Congruum

   Equivalently, the two annuli between the three yellow circles have equal areas, π times the congruum. In number theory, a congruum (plural congrua) is the difference between successive square numbers in an arithmetic progression of three squares. That is, if , , and (for integers , , and ) are three square numbers that are equally spaced apart ...

6. Isometry - Wikipedia

   en.wikipedia.org/wiki/Isometry

   In mathematics, an isometry (or congruence, or congruent transformation) is a distance -preserving transformation between metric spaces, usually assumed to be bijective. [a] The word isometry is derived from the Ancient Greek: ἴσος isos meaning "equal", and μέτρον metron meaning "measure". If the transformation is from a metric space ...

7. Hinge theorem - Wikipedia

   en.wikipedia.org/wiki/Hinge_theorem

   Hinge theorem. In geometry, the hinge theorem (sometimes called the open mouth theorem) states that if two sides of one triangle are congruent to two sides of another triangle, and the included angle of the first is larger than the included angle of the second, then the third side of the first triangle is longer than the third side of the ...