"Triangle postulate" redirects here. Not to be confused with Triangle inequality.
"Angle sum theorem" redirects here. For trigonometric identities concerning sums of angles, see List of trigonometric identities § Angle sum and difference identities.
In a Euclidean space, the sum of angles of a triangle equals the straight angle (180 degrees, π radians, two right angles, or a half-turn).
A triangle has three angles, one at each vertex, bounded by a pair of adjacent sides.
It was unknown for a long time whether other geometries exist, for which 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.
Equivalence of the parallel postulate and the "sum of the angles equals to 180°" statement
and 27 Related for: Sum of angles of a triangle information
states that the measure of an exterior angleofatriangle is equal to the sumof the measures of the remote interior angles. This result, which depends...
A right triangle or right-angledtriangle, sometimes called an orthogonal triangle or rectangular triangle, is atriangle in which two sides are perpendicular...
obtuse-angled triangle) is a triangle with one obtuse angle (greater than 90°) and two acute angles. Since atriangle'sangles must sum to 180° in Euclidean geometry...
Lehmann, Ingmar. The Secrets ofTriangles, Prometheus Books, 2012. Internal anglesofatriangle Interior anglesumof polygons: a general formula - Provides...
internal angles, measured here in degrees. A right triangle (or right-angledtriangle) has one of its interior angles measuring 90° (a right angle). The...
mathematics, the triangle inequality states that for any triangle, the sumof the lengths of any two sides must be greater than or equal to the length of the remaining...
functions of one or more angles. They are distinct from triangle identities, which are identities potentially involving angles but also involving side...
parallelogram are of equal length and the opposite anglesofa parallelogram are of equal measure. The congruence of opposite sides and opposite angles is a direct...
internal angles are also congruent to each other and are each 60°. It is also a regular polygon, so it is also referred to as a regular triangle. Denoting...
In geometry, calculating the area ofatriangle is an elementary problem encountered often in many different situations. The best known and simplest formula...
any sumof two angles in atriangle is supplementary to the third because the sumof the internal anglesofatriangle is a straight angle. Two angles that...
ABC. The proof of similarity of the triangles requires the triangle postulate: The sumof the angles in atriangle is two right angles, and is equivalent...
so that its endpoint is on a line and the adjacent angles are equal, then they are right angles. The term is a calque of Latin angulus rectus; here rectus...
would sum to at least 180°, the total of all angles in any Euclidean triangle. Since atriangle is obtuse or right if and only if one of its angles is obtuse...
Solution oftriangles (Latin: solutio triangulorum) is the main trigonometric problem of finding the characteristics ofatriangle (angles and lengths of sides)...
to solve for arbitrary angles. However, some special angles can be trisected: for example, it is trivial to trisect a right angle. It is possible to trisect...
a hyperbolic triangle is atriangle in the hyperbolic plane. It consists of three line segments called sides or edges and three points called angles or...
pass through the point P. Consequently, the sumofangles in atriangle is less than 180° and the ratio ofa circle's circumference to its diameter is greater...
(trígōnon) 'triangle', and μέτρον (métron) 'measure') is a branch of mathematics concerned with relationships between angles and side lengths oftriangles. In...
incircle is atriangle center called the triangle's incenter. An excircle or escribed circle of the triangle is a circle lying outside the triangle, tangent...
the angle between the crank and the rod is not a right angle. Summing the anglesof the triangle 88.21738° + 18.60647° + 73.17615° gives 180.00000°. A single...
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