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  2. Taxicab geometry - Wikipedia

    en.wikipedia.org/wiki/Taxicab_geometry

    Taxicab geometry or Manhattan geometry is geometry where the familiar Euclidean distance is ignored, and the distance between two points is instead defined to be the sum of the absolute differences of their respective Cartesian coordinates, a distance function (or metric) called the taxicab distance, Manhattan distance, or city block distance.

  3. Euclidean geometry - Wikipedia

    en.wikipedia.org/wiki/Euclidean_geometry

    Congruence of triangles is determined by specifying two sides and the angle between them (SAS), two angles and the side between them (ASA) or two angles and a corresponding adjacent side (AAS). Specifying two sides and an adjacent angle (SSA), however, can yield two distinct possible triangles unless the angle specified is a right angle.

  4. 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 ...

  5. Hilbert's axioms - Wikipedia

    en.wikipedia.org/wiki/Hilbert's_axioms

    Hilbert's axioms are a set of 20 assumptions proposed by David Hilbert in 1899 in his book Grundlagen der Geometrie [1][2][3][4] (tr. The Foundations of Geometry) as the foundation for a modern treatment of Euclidean geometry. Other well-known modern axiomatizations of Euclidean geometry are those of Alfred Tarski and of George Birkhoff.

  6. Similarity (geometry) - Wikipedia

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

    Two triangles, ABC and A'B'C' are similar if and only if corresponding angles have the same measure: this implies that they are similar if and only if the lengths of corresponding sides are proportional. [1] It can be shown that two triangles having congruent angles (equiangular triangles) are similar, that is, the corresponding sides can be ...

  7. Food poisoning dangers are real after severe weather. Here’s ...

    www.aol.com/news/food-poisoning-dangers-real...

    Food stored in a freezer at 0 degrees Fahrenheit is safe to re-freeze or cook as long as it doesn’t rise above that crucial 40-degree mark, according to the CDC. Once the power is cut, a full ...

  8. Law of cosines - Wikipedia

    en.wikipedia.org/wiki/Law_of_cosines

    Law of cosines. Fig. 1 – A triangle. The angles α (or A), β (or B), and γ (or C) are respectively opposite the sides a, b, and c. In trigonometry, the law of cosines (also known as the cosine formula or cosine rule) relates the lengths of the sides of a triangle to the cosine of one of its angles. For a triangle with sides and opposite ...

  9. Georgia prisons 'horrific and unsafe' with homicides rampant ...

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    Georgia prisons feature in “horrific and unsafe conditions” that violate the Constitution’s protection against cruel and unusual DOJ alleged Tuesday.

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