Start by reviewing Example 5.1 (proving the perpendicular bisectors are concurrent).

The general trick is the following:

• Start with two angle bisectors, say of $A$ and $B$ we know these two lines intersect at one point (call it $G$).
• Connect $C$ to $G$, our goal now is to prove that $\overline{CG}$ is actually an angle bisector as well.

Hint: Try to use congruent triangles to help.