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2. Congruence (geometry) - Wikipedia

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

   Congruence (geometry) Relationship between two figures of the same shape and size, or mirroring each other. The two triangles on the left are congruent. The third is similar to them. The last triangle is neither congruent nor similar to any of the others. Congruence permits alteration of some properties, such as location and orientation, but ...

3. Congruence relation - Wikipedia

   en.wikipedia.org/wiki/Congruence_relation

   Congruence relation. In abstract algebra, a congruence relation (or simply congruence) is an equivalence relation on an algebraic structure (such as a group, ring, or vector space) that is compatible with the structure in the sense that algebraic operations done with equivalent elements will yield equivalent elements. [1]

4. Corresponding sides and corresponding angles - Wikipedia

   en.wikipedia.org/wiki/Corresponding_sides_and...

   In geometry, the tests for congruence and similarity involve comparing corresponding sides and corresponding angles of polygons. In these tests, each side and each angle in one polygon is paired with a side or angle in the second polygon, taking care to preserve the order of adjacency. [1] For example, if one polygon has sequential sides a, b ...

5. Similarity (geometry) - Wikipedia

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

   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 ...

6. 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 ...

7. Table of congruences - Wikipedia

   en.wikipedia.org/wiki/Table_of_congruences

   Clement's congruence-based theorem characterizes the twin primes pairs of the form through the following conditions: P. A. Clement's original 1949 paper [ 2] provides a proof of this interesting elementary number theoretic criteria for twin primality based on Wilson's theorem. Another characterization given in Lin and Zhipeng's article provides ...