9.2. Properties of Arcs http://www.ck12.org
Solution:From the picture, we see that^6 ACDand^6 ECBare vertical angles.^6 DCBand^6 ACEare also vertical
angles. Because all vertical angles are equal and these four angles are all central angles, we know thatAD̂∼=EB̂and
AÊ∼=DB̂.
Example 4:Are the blue arcs congruent? Explain why or why not.
a)
b)
Solution:In part a,AD̂∼=BĈbecause they have the same central angle measure. In part b, the two arcs do have the
same measure, but are not congruent because the circles are not congruent.
Arc Addition Postulate
Just like the Angle Addition Postulate and the Segment Addition Postulate, there is an Arc Addition Postulate. It is
very similar.
Arc Addition Postulate:The measure of the arc formed by two adjacent arcs is the sum of the measures of the two
arcs.
Using the picture from Example 3, we would saymAÊ+mEB̂=mAEB̂.
Example 5:Reusing the figure from Example 2, find the measure of the following arcs in
⊙
A.EBis a diameter.