Geometry: Common Core (15th Edition)

$C$
The definition of bisecting is that something is cut in two equal portions. If $\overline {BD}$ bisects $\angle ABC$, then $\overline {BD}$ cuts $\angle ABC$ into exactly two congruent angles. In the answer options, only option $C$ shows that $\angle ABC$ is cut into exactly two congruent angles: $\angle ABD$ and $\angle CBD$. These angles are marked as being congruent in the diagram.