How do we construct an angle bisector?

You will need a compass and straightedge.

Angle bisector: Divides angle into two congruent adjacent angles

Step 1: Using your straightedge, create an angle. Label the angle ABC.

                    

Step 2: Place the needle of the compass on point B and draw an are on line BC and label it point S. Draw another arc on line BC and label that point T.

Step 3: Using the same distance of the compass, place the needle at point S and make an arc on the interior of triangle ABC. Repeat the same thing to point T and make sure both arcs intersect. 

                  

Step 4: Draw a line from point B to the point of the intersecting arcs. 

                                                

http://www.onlinemathlearning.com/angle-bisector.html