1. The problem states that $AD \cong CD$, meaning segment $AD$ is congruent to segment $CD$. 2. Point $D$ lies on segment $AC$, and $BD$ is a segment drawn from vertex $B$ to point $D$ on $AC$. 3. Since $AD$ and $CD$ are congruent, point $D$ is the midpoint of segment $AC$. 4. A segment drawn from a vertex to the midpoint of the opposite side is called a **median**. 5. Therefore, segment $BD$ is a median of triangle $ABC$. Final answer: $BD$ is a median.