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  2. Exterior angle theorem - Wikipedia

    en.wikipedia.org/wiki/Exterior_angle_theorem

    The exterior angle theorem is not valid in spherical geometry nor in the related elliptical geometry. Consider a spherical triangle one of whose vertices is the North Pole and the other two lie on the equator. The sides of the triangle emanating from the North Pole (great circles of the sphere) both meet the equator at right angles, so this ...

  3. Absolute geometry - Wikipedia

    en.wikipedia.org/wiki/Absolute_geometry

    In Euclid's Elements, the first 28 Propositions and Proposition 31 avoid using the parallel postulate, and therefore are valid in absolute geometry.One can also prove in absolute geometry the exterior angle theorem (an exterior angle of a triangle is larger than either of the remote angles), as well as the Saccheri–Legendre theorem, which states that the sum of the measures of the angles in ...

  4. List of triangle topics - Wikipedia

    en.wikipedia.org/wiki/List_of_triangle_topics

    Droz-Farny line theorem; Encyclopedia of Triangle Centers; Equal incircles theorem; Equal parallelians point; Equidissection; Equilateral triangle; Euler's line; Euler's theorem in geometry; Erdős–Mordell inequality; Exeter point; Exterior angle theorem; Fagnano's problem; Fermat point; Fermat's right triangle theorem; Fuhrmann circle ...

  5. Internal and external angles - Wikipedia

    en.wikipedia.org/wiki/Internal_and_external_angles

    If every internal angle of a simple polygon is less than a straight angle (π radians or 180°), then the polygon is called convex. In contrast, an external angle (also called a turning angle or exterior angle) is an angle formed by one side of a simple polygon and a line extended from an adjacent side. [1]: pp. 261–264

  6. Heron's formula - Wikipedia

    en.wikipedia.org/wiki/Heron's_formula

    There are many ways to prove Heron's formula, for example using trigonometry as below, or the incenter and one excircle of the triangle, [7] or as a special case of De Gua's theorem (for the particular case of acute triangles), [8] or as a special case of Brahmagupta's formula (for the case of a degenerate cyclic quadrilateral).

  7. Category:Theorems about triangles - Wikipedia

    en.wikipedia.org/wiki/Category:Theorems_about...

    Main page; Contents; Current events; Random article; About Wikipedia; Contact us; Pages for logged out editors learn more

  8. Starbucks union votes to authorize strike ahead of last ...

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    Starbucks Workers United said Tuesday that 98% of union baristas have voted to authorize a strike as they seek a contract with the coffee giant.

  9. NYPD’s $400K-a-year top earner Quathisha Epps is retiring ...

    www.aol.com/nypd-400k-top-earner-quathisha...

    Epps, 51, also faced an internal affairs investigation into her overtime, sources said. Records showed that last year she worked nearly 1,627 hours of overtime on top of her regular shift, or an ...