Question

What is the relationship between segment EB and segment FB in the construction of an angle bisector?

Answer 1

See the diagram.

We want to have the bisector for the angle at point B ie., angle FBE.

First we mark E and F by using compass and drawing arcs cutting the lines at equal distances (x units).   Then From E and F, draw arcs of equal radii 'y'. The points H and G of the intersections of the arcs will be on the bisector.

So join B, H , G to get the angular bisector.

Segments  FB and  EB are equal in length.