bisektor

Bisektor, in geometry, refers to a line, ray, or segment that divides another figure or measure into two equal parts. The term is commonly used for two main kinds: angle bisectors and segment bisectors. An angle bisector cuts one angle into two congruent angles, while a segment bisector intersects a segment at its midpoint. A related concept is the perpendicular bisector, a line that is both perpendicular to a segment and passes through its midpoint.

An angle bisector has two notable properties. First, any point on the internal angle bisector is equidistant from the two sides of the angle, and similarly for the external angle bisector with the opposite orientation. In triangles, the Angle Bisector Theorem states that if a point D lies on the opposite side BC of triangle ABC and AD is the angle bisector of angle A, then BD/DC equals AB/AC. This ratio gives a precise division of the opposite side. Angle bisectors can be constructed with compass and straightedge by intersecting arcs drawn from the angle’s sides.

A perpendicular bisector is the locus of points equidistant from the endpoints of a given segment, and it is perpendicular to that segment at its midpoint. In triangle geometry, the three perpendicular bisectors meet at the circumcenter, the center of the triangle’s circumscribed circle.

A segment bisector is any line or segment that passes through the midpoint of a given segment, thereby dividing it into two equal parts. Bisectors have broad applications in geometric constructions, surveying, computer graphics, and design, where precise proportional divisions are essential.