From the word itself, an angle bisector is a line segment that divides the angle into two equal parts. Take this problem for example. The angle is FGI, which means that the vertex is at point G. Hence, you create a line segment from vertex and extend it towards point H, so it forms a line segment GH. The H must be on the same plane but situated on the same side of point F and I.
Suppose the angle FGI is 80°. Then, if the angle bisector is drawn, two 40° angles are drawn: angle FGH and HGI. These angles are situated side by side together.
