Learning Resources
Investigation 4: Angles and Arcs
You are probably already familiar with the term arc. It is nothing more than a segment or piece of a curve. In our case the curve is a circle. If the arc is half the circle, it is called a semi-circle. The diagram below shows two semi-circles, the red arc and the blue arc..
To name a semi-circle requires three letters. This is necessary in order to avoid confusion about which arc is being referred to. For example in the above diagram, if we simply use 
we do not know if we are referring to the red or blue arc. To refer to the red arc we would use the notation 
and for the blue arc we would use 
The diagrams below show two different arcs which are not semi-circles. The red one on the left is called a minor arc, the blue one on the right is called a major arc. It should be fairly obvious that minor refers to arcs less than a semi-circle and major refers to arcs that are greater than a semi-circle.
Minor arcs can be named using just two letters. In the diagrams above, if we write it automatically assumes we mean the minor arc. That is the convention that is used in all mathematics texts. If we wish to refer to the major arc, we must put a point on it and use three letters. Thus in the diagrams above we have no way of naming the major arc in the one on the left. In the diagram on the right we can write for the major arc.
We now need to turn our attention to how to measure these arcs. That is done on the next page.