1. **State the problem:** Given triangle ABC with BD as the bisector of segment AC, prove that triangle ABD is congruent to triangle CBD using a flowchart proof. 2. **Identify given information:** BD bisects AC, so D is the midpoint of AC. This means $AD = DC$. 3. **List what to prove:** Prove $\triangle ABD \cong \triangle CBD$. 4. **Use the properties and theorems:** - Since D is midpoint, $AD = DC$ (definition of midpoint). - BD is common to both triangles (shared side). - Angle ABD and angle CBD are vertical angles and thus congruent. 5. **Apply the Side-Angle-Side (SAS) congruence postulate:** - $AD = DC$ (given by midpoint) - $\angle ABD = \angle CBD$ (vertical angles) - $BD = BD$ (common side) 6. **Conclusion:** By SAS, $\triangle ABD \cong \triangle CBD$. This completes the flowchart proof.