In geometry, an angle is considered “included” when it is formed by two sides of a polygon that are also specified in a particular context. More precisely, when referencing two sides of a triangle, quadrilateral, or other polygon, the included angle is the angle whose vertex is the point where those two sides meet. For instance, in triangle ABC, the angle at vertex B is the included angle between sides AB and BC.
The concept of an included angle is fundamental in various geometric theorems and proofs. Its significance lies in providing a direct relationship between sides and angles within geometric figures. This relationship is critical for determining congruence and similarity, enabling calculations of areas and other properties, and facilitating solutions to problems involving geometric figures. Historically, the understanding of this relationship has been pivotal in fields such as surveying, architecture, and engineering, where precise geometric calculations are essential.
