Szögfelezk

Szögfelezk, also known as angle bisector, is a line or ray that divides an angle into two equal parts. It is a fundamental concept in geometry, particularly in the study of triangles and other polygons. The angle bisector theorem states that the angle bisector of a triangle divides the opposite side into segments that are proportional to the other two sides of the triangle. This theorem is crucial in solving various geometric problems and proving congruence and similarity of triangles.

In a right triangle, the angle bisector of the right angle is also the median and the altitude, as it divides the hypotenuse into two equal segments. The concept of angle bisectors is also extended to other geometric shapes, such as circles, where the angle bisector of a central angle divides the arc it intercepts into two equal parts.

The angle bisector of a triangle can be constructed using various methods, including the use of a compass and straightedge. It is an essential tool in geometric constructions and proofs, helping to establish relationships between angles and sides of polygons. The study of angle bisectors is a key area in Euclidean geometry, contributing to the understanding of geometric properties and relationships.