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Sum_of_angles_of_a_triangle abstract "In several geometries, a triangle has three vertices and three sides, where three angles of a triangle are formed at each vertex by a pair of adjacent sides. In a Euclidean space, the sum of measures of these three angles of any triangle is invariably equal to the straight angle, also expressed as 180°, π radians, two right angles, or a half-turn. It was unknown for a long time whether other geometries exist, where this sum is different. The influence of this problem on mathematics was particularly strong during the 19th century. Ultimately, the answer was proven to be positive: in other spaces (geometries) this sum can be greater or lesser, but it then must depend on the triangle. Its difference from 180° is a case of angular defect and serves as an important distinction for geometric systems.".
Sum_of_angles_of_a_triangle thumbnail Triangle_angles_sum_to_180_degrees.svg?width=300.
Sum_of_angles_of_a_triangle wikiPageID "5407025".
Sum_of_angles_of_a_triangle wikiPageLength "6991".
Sum_of_angles_of_a_triangle wikiPageOutDegree "45".
Sum_of_angles_of_a_triangle wikiPageRevisionID "695676802".
Sum_of_angles_of_a_triangle wikiPageWikiLink Angle.
Sum_of_angles_of_a_triangle wikiPageWikiLink Angular_defect.
Sum_of_angles_of_a_triangle wikiPageWikiLink Area.
Sum_of_angles_of_a_triangle wikiPageWikiLink Category:Geometry.
Sum_of_angles_of_a_triangle wikiPageWikiLink Category:Triangle_geometry.
Sum_of_angles_of_a_triangle wikiPageWikiLink Circle.
Sum_of_angles_of_a_triangle wikiPageWikiLink Convex_polygon.
Sum_of_angles_of_a_triangle wikiPageWikiLink Curvature.
Sum_of_angles_of_a_triangle wikiPageWikiLink Curve.
Sum_of_angles_of_a_triangle wikiPageWikiLink Degree_(angle).
Sum_of_angles_of_a_triangle wikiPageWikiLink Differential_geometry_of_surfaces.
Sum_of_angles_of_a_triangle wikiPageWikiLink Distance.
Sum_of_angles_of_a_triangle wikiPageWikiLink Edge_(geometry).
Sum_of_angles_of_a_triangle wikiPageWikiLink Euclidean_geometry.
Sum_of_angles_of_a_triangle wikiPageWikiLink Euclidean_space.
Sum_of_angles_of_a_triangle wikiPageWikiLink Euclids_Elements.
Sum_of_angles_of_a_triangle wikiPageWikiLink Exterior_angle_theorem.
Sum_of_angles_of_a_triangle wikiPageWikiLink Foundations_of_geometry.
Sum_of_angles_of_a_triangle wikiPageWikiLink Gauss–Bonnet_theorem.
Sum_of_angles_of_a_triangle wikiPageWikiLink Hilberts_axioms.
Sum_of_angles_of_a_triangle wikiPageWikiLink Hyperbolic_geometry.
Sum_of_angles_of_a_triangle wikiPageWikiLink Ideal_triangle.
Sum_of_angles_of_a_triangle wikiPageWikiLink Johann_Heinrich_Lambert.
Sum_of_angles_of_a_triangle wikiPageWikiLink Lambert_quadrilateral.
Sum_of_angles_of_a_triangle wikiPageWikiLink List_of_geometry_topics.
Sum_of_angles_of_a_triangle wikiPageWikiLink Measure_(mathematics).
Sum_of_angles_of_a_triangle wikiPageWikiLink Omar_Khayyam.
Sum_of_angles_of_a_triangle wikiPageWikiLink Parallel_postulate.
Sum_of_angles_of_a_triangle wikiPageWikiLink Pi.
Sum_of_angles_of_a_triangle wikiPageWikiLink Playfairs_axiom.
Sum_of_angles_of_a_triangle wikiPageWikiLink Pythagorean_theorem.
Sum_of_angles_of_a_triangle wikiPageWikiLink Radian.
Sum_of_angles_of_a_triangle wikiPageWikiLink Right_angle.
Sum_of_angles_of_a_triangle wikiPageWikiLink Saccheri_quadrilateral.
Sum_of_angles_of_a_triangle wikiPageWikiLink Spherical_trigonometry.
Sum_of_angles_of_a_triangle wikiPageWikiLink Summation.
Sum_of_angles_of_a_triangle wikiPageWikiLink Support_(mathematics).
Sum_of_angles_of_a_triangle wikiPageWikiLink Triangle.
Sum_of_angles_of_a_triangle wikiPageWikiLink Turn_(geometry).
Sum_of_angles_of_a_triangle wikiPageWikiLink Vertex_(geometry).
Sum_of_angles_of_a_triangle wikiPageWikiLink File:Triangle_angles_sum_to_180_degrees.svg.
Sum_of_angles_of_a_triangle wikiPageWikiLink File:Triangle_somme_des_angles.png.
Sum_of_angles_of_a_triangle wikiPageWikiLinkText "Sum of angles of a triangle".
Sum_of_angles_of_a_triangle wikiPageWikiLinkText "sum of angles of a triangle".
Sum_of_angles_of_a_triangle wikiPageWikiLinkText "sum of the angles".
Sum_of_angles_of_a_triangle wikiPageWikiLinkText "sum of the measures of the interior angles of a triangle".
Sum_of_angles_of_a_triangle wikiPageUsesTemplate Template:Expand_section.
Sum_of_angles_of_a_triangle wikiPageUsesTemplate Template:Main.
Sum_of_angles_of_a_triangle wikiPageUsesTemplate Template:Redirect-distinguish.
Sum_of_angles_of_a_triangle wikiPageUsesTemplate Template:See_also.
Sum_of_angles_of_a_triangle subject Category:Geometry.
Sum_of_angles_of_a_triangle subject Category:Triangle_geometry.
Sum_of_angles_of_a_triangle type Thing.
Sum_of_angles_of_a_triangle comment "In several geometries, a triangle has three vertices and three sides, where three angles of a triangle are formed at each vertex by a pair of adjacent sides. In a Euclidean space, the sum of measures of these three angles of any triangle is invariably equal to the straight angle, also expressed as 180°, π radians, two right angles, or a half-turn. It was unknown for a long time whether other geometries exist, where this sum is different.".
Sum_of_angles_of_a_triangle label "Sum of angles of a triangle".
Sum_of_angles_of_a_triangle seeAlso Triangle.
Sum_of_angles_of_a_triangle differentFrom Triangle_inequality.
Sum_of_angles_of_a_triangle sameAs Q7840113.
Sum_of_angles_of_a_triangle sameAs Vinkelsum.
Sum_of_angles_of_a_triangle sameAs Winkelsumme.
Sum_of_angles_of_a_triangle sameAs Somme_des_angles_dun_triangle.
Sum_of_angles_of_a_triangle sameAs m.0cc9xpf.
Sum_of_angles_of_a_triangle sameAs Збир_углова_у_троуглу.
Sum_of_angles_of_a_triangle sameAs Vinkelsumma.
Sum_of_angles_of_a_triangle sameAs Q7840113.
Sum_of_angles_of_a_triangle wasDerivedFrom Sum_of_angles_of_a_triangle?oldid=695676802.
Sum_of_angles_of_a_triangle depiction Triangle_angles_sum_to_180_degrees.svg.
Sum_of_angles_of_a_triangle isPrimaryTopicOf Sum_of_angles_of_a_triangle.