In a Euclidean space, the sum of angles of a triangle equals a straight angle (180 degrees, π radians, two right angles, or a half-turn). A triangle has...

A triangle has three internal angles, each one bounded by a pair of adjacent edges; the sum of angles of a triangle always equals a straight angle (180...

states that the measure of an exterior angle of a triangle is equal to the sum of the measures of the remote interior angles. This result, which depends...

A right triangle or right-angled triangle, sometimes called an orthogonal triangle or rectangular triangle, is a triangle in which two sides are perpendicular...

Lehmann, Ingmar. The Secrets of Triangles, Prometheus Books, 2012. Internal angles of a triangle Interior angle sum of polygons: a general formula - Provides...

obtuse-angled triangle) is a triangle with one obtuse angle (greater than 90°) and two acute angles. Since a triangle's angles must sum to 180° in Euclidean geometry...

mathematics, the triangle inequality states that for any triangle, the sum of the lengths of any two sides must be greater than or equal to the length of the remaining...

Angle-based special right triangles are specified by the relationships of the angles of which the triangle is composed. The angles of these triangles...

triangles are congruent. AAS is equivalent to an ASA condition, by the fact that if any two angles are given, so is the third angle, since their sum should...

functions of one or more angles. They are distinct from triangle identities, which are identities potentially involving angles but also involving side...

In geometry, calculating the area of a triangle is an elementary problem encountered often in many different situations. The best known and simplest formula...

parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure. The congruence of opposite sides and opposite angles is a direct...

ABC. The proof of similarity of the triangles requires the triangle postulate: The sum of the angles in a triangle is two right angles, and is equivalent...

right angle. Let A, B, C denote the vertices and also the angles of the triangle, and let a = | B C ¯ | , b = | C A ¯ | , c = | A B ¯ | {\displaystyle a=\left|{\overline...

example, a proof of the theorem on the sum of angles of a triangle can be done by adding a straight line parallel to one of the triangle sides (passing...

<A+B+C<3\pi } (Todhunter, Art.22,32). In particular, the sum of the angles of a spherical triangle is strictly greater than the sum of the angles of a...

An equilateral triangle is a triangle in which all three sides have the same length, and three angles are equal. Because of these properties, the equilateral...

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...

Euclidean triangles, where the angles always add up to π radians (180°, a straight angle), in hyperbolic space the sum of the angles of a triangle is always...

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...

golden triangle is an acute (isosceles) triangle. Since the angles of a triangle sum to π {\displaystyle \pi } radians, each of the base angles (CBX and...

a hyperbolic triangle is a triangle in the hyperbolic plane. It consists of three line segments called sides or edges and three points called angles or...

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...

would sum to at least 180°, the total of all angles in any Euclidean triangle. Since a triangle is obtuse or right if and only if one of its angles is obtuse...

any sum of two angles in a triangle is supplementary to the third because the sum of the internal angles of a triangle is a straight angle. Two angles that...

incircle is a triangle center called the triangle's incenter. An excircle or escribed circle of the triangle is a circle lying outside the triangle, tangent...

pass through the point P. Consequently, the sum of angles in a triangle is less than 180° and the ratio of a 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 of triangles. In...

parameters in a triangle inequality can be the side lengths, the semiperimeter, the angle measures, the values of trigonometric functions of those angles, the...

the angle between the crank and the rod is not a right angle. Summing the angles of the triangle 88.21738° + 18.60647° + 73.17615° gives 180.00000°. A single...