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The congruence theorems side-angle-side (SAS) and side-side-side (SSS) also hold on a sphere; in addition, if two spherical triangles have an identical angle-angle-angle (AAA) sequence, they are congruent (unlike for plane triangles). [9] The plane-triangle congruence theorem angle-angle-side (AAS) does not hold for spherical triangles. [10]
Three sides (SSS) Two sides and the included angle (SAS, side-angle-side) Two sides and an angle not included between them (SSA), if the side length adjacent to the angle is shorter than the other side length. A side and the two angles adjacent to it (ASA) A side, the angle opposite to it and an angle adjacent to it (AAS).
The prime pairs of the form (, +) for some include the special cases of the cousin primes (when =) and the sexy primes (when =). We have elementary congruence-based characterizations of the primality of such pairs, proved for instance in the article. [3]
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Download as PDF; Printable version; In other projects Wikidata item; Appearance. move to sidebar hide. Side-side-side is a means of ... (SSS) SSS postulate
Tarski's system has the unusual property that all sentences can be written in universal-existential form, a special case of the prenex normal form. This form has all universal quantifiers preceding any existential quantifiers , so that all sentences can be recast in the form ∀ u ∀ v … ∃ a ∃ b … . {\displaystyle \forall u\forall v ...
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 second triangle. [1]
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.