angle bisector
cuts an angle perfectly in half
An angle bisector is a line or a ray that divides an angle into two congruent angles. In other words, an angle bisector divides the angle into two equal parts, each of which measures half of the original angle. The point where the angle bisector meets the opposite side of the angle is called the point of angle bisector.
The angle bisector theorem states that a line segment drawn from the vertex of an angle to the point on the opposite side that divides the angle into two congruent angles is proportional to the lengths of the two segments on either side of the angle. That is, if a line bisects an angle, it divides the opposite side into two segments whose lengths are proportional to the lengths of the other two sides of the angle.
There are many applications of angle bisectors in geometry, including finding the length of a side of a triangle, determining congruence between two angles, and solving problems involving triangles and quadrilaterals. Overall, angle bisectors are an important tool in geometry that help to solve many problems related to angles and their properties.
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