A triangle is a three-sided polygon with three edges and three vertices. It is one of the simplest and most fundamental shapes in geometry.

Triangles can be classified by their sides and angles. An equilateral triangle has all sides of equal length, an isosceles triangle has two sides of equal length, and a scalene triangle has all sides of different lengths. Regarding angles, a right triangle has one angle of exactly 90 degrees, an acute triangle has all angles less than 90 degrees, and an obtuse triangle has one angle greater than 90 degrees.

In Euclidean space, the sum of the internal angles of any triangle always equals 180 degrees. This property is often used in geometric proofs and calculations.

The study of triangles and the relationships between their sides and angles is known as trigonometry, which has wide-ranging applications in fields such as physics, engineering, and computer graphics.

An angle is a measure of rotation or turning and is usually measured in degrees or radians. In geometry, an angle is the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex. The size of an angle is determined by the amount of rotation from one ray to the other.

A right triangle (or right-angled triangle) is a triangle in which one of the angles is a right angle (90 degrees). The side opposite the right angle is called the hypotenuse, and it is the longest side. The other two sides are known as the adjacent and opposite sides, relative to the non-right angle being referenced.