Constructing an angle bisector

This is the very first post of this blog, and it will be on angle bisectors, and how to construct one.

What is an angle bisector?
To bisect something is to divide it into two.
Therefore, an angle bisector is a line which divides the angle into two equal angles. An angle only has one bisector. Each point of an angle bisector is equidistant from the sides of the angle.

How to construct an angle bisector?
To bisect an angle with a compass, you must draws a circle whose center is the vertex of the angle. The circle meets the angle at two points: one on each leg. Using each of these points as a center, draw two circles of the same size. The intersection of the circles (two points) determines a line that is the angle bisector.

Sounds complicated? Let the following videos guide you.

Note: there are various ways to bisecting an angle

Way 1


Way 2


Note: It is important that you do not change the width of the compass when drawing the arc, otherwise it will be inaccurate.

It is also interesting to know that trisection of an angle (dividing it into three equal parts) cannot be achieved with the ruler and compass alone. However it can be done with other methods. I will post about this later on, if i have the time.

Credits:
http://www.youtube.com/watch?v=2dhB6HHLBGM
http://www.youtube.com/watch?v=ug3TasAxvOk
http://en.wikipedia.org/wiki/Bisection