Angle bisector

An angle bisector is a ray that divides an angle into two equal angles. In a triangle, the three internal angle bisectors meet at the incenter.

Angle: A geometric figure formed by two rays sharing a common endpoint. An angle bisector divides this figure into two equal parts.
Compass-and-straightedge construction: A geometric construction using only an unmarked straightedge and a compass. It constructs an angle bisector by intersecting equal-radius arcs.
Incenter: The point where a triangle's three internal angle bisectors intersect. It is the shared intersection produced by a triangle's angle bisectors.
Median (geometry): A segment joining a triangle's vertex to the midpoint of the opposite side. A median bisects a side, not necessarily the angle at its vertex.
Ray (geometry): A part of a line that starts at an endpoint and extends infinitely in one direction. An angle bisector is a ray whose endpoint is the angle's vertex.
Angle bisector theorem: A triangle theorem stating that an angle bisector divides the opposite side in the ratio of the adjacent sides. It translates the bisected angle into a precise side-length ratio.
Incircle: The largest circle contained in a polygon, tangent to every side; for a triangle, it is centered at the incenter. The incenter locates the circle equally tangent to all three triangle sides.
Altitude (triangle): A perpendicular segment from a triangle's vertex to the line containing the opposite side. An altitude is defined by perpendicularity rather than equal angle measures.
Angle measure: A numerical measure of the rotation or opening between two rays, commonly expressed in degrees or radians. The two angles formed by a bisector have equal measure.
Distance from a point to a line: The length of the perpendicular segment from a point to a line. Points on an angle bisector are equidistant from the angle's sides.

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