angle bisector
a ray that divides an angle into two congruent angles
An angle bisector is a line or a ray that divides an angle into two equal parts or angles. It is also sometimes referred to as a bisector of an angle. An angle bisector starts from the vertex of the angle and extends to the opposite side or to the adjacent sides of the angle.
In a triangle, the angle bisectors of the three interior angles meet at a single point called the incenter. The incenter is the center of the triangle’s incircle, which is a circle that is tangent to all three sides of the triangle.
The angle bisector theorem states that for any given triangle, the length of the intersection of the angle bisector with the opposite side is proportional to the lengths of the other two sides of the triangle. Mathematically, this can be expressed as follows:
– If a line bisects an angle of a triangle and intersects the opposite side at a point, then that point divides the opposite side into segments whose lengths are proportional to the lengths of the other two sides of the triangle.
The angle bisector is a useful tool in various branches of mathematics, including geometry, trigonometry, and calculus.
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