Which geometric object is defined as the set of all points in a plane that are equidistant from the two sides of a given angle?

The geometric object defined as the set of all points in a plane that are equidistant from the two sides of a given angle is called the angle bisector. The angle bisector is a line that splits the angle into two equal parts, and every point on this line is equidistant from the two sides of the angle.

Geometrically, if you have an angle formed by two lines that meet at a vertex, the angle bisector is the line that passes through the vertex and divides the angle into two equal angles. This concept is widely used in various geometric constructions and proofs, including the properties of triangles and other polygonal shapes. In practical applications, understanding angle bisectors is essential in fields that require precise measurements, such as architecture and engineering.