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...

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

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...

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...

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...

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...

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 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...

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...

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

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

<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...

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...

complementary angles are adjacent, their non-shared sides form a right angle. In a right-angle triangle the two acute angles are complementary as the sum of the...

C E {\displaystyle \angle BAE\cong \angle DCE} (alternate interior angles are equal in measure). (since these are angles that a transversal makes with...

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...

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...

the sides of any triangle to the sines of its angles. According to the law, a sin ⁡ α = b sin ⁡ β = c sin ⁡ γ = 2 R , {\displaystyle {\frac {a}{\sin {\alpha...

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...

underlying topology. In the simplest application, the case of a triangle on a plane, the sum of its angles is 180 degrees. The Gauss–Bonnet theorem extends this...

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...

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...

(trígōnon) 'triangle' and μέτρον (métron) 'measure') is a branch of mathematics concerned with relationships between angles and side lengths of triangles. In...

In geometry, an altitude of a triangle is a line segment through a given vertex (called apex) and perpendicular to a line containing the side or edge...

used: the sum of the angles in a triangle is equal to 180° and the base angles of an isosceles triangle are equal. Provided AC is a diameter, angle at B is...

to remember these definitions. In a right-angled triangle, the sum of the two acute angles is a right angle, that is, 90° or ⁠π/2⁠ radians. Therefore...

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...