1. **State the problem:** Given that segment $\overline{AC}$ bisects segment $\overline{BD}$, complete the flowchart proof to show that $\triangle ABE \cong \triangle CDE$. 2. **Understand the definition of bisector:** If $\overline{AC}$ bisects $\overline{BD}$ at point $E$, then $E$ is the midpoint of $\overline{BD}$, so $\overline{BE} \cong \overline{ED}$. 3. **Given information:** $\overline{AC}$ bisects $\overline{BD}$ (Given). 4. **From the bisector definition:** $\overline{BE} \cong \overline{ED}$ (A midpoint divides a segment into two congruent segments). 5. **Given:** $\overline{AE} \cong \overline{EC}$ (Because $E$ is on $\overline{AC}$ and divides it into two segments). 6. **Vertical angles:** $\angle BEA \cong \angle CED$ (Vertical angles formed by intersecting lines are congruent). 7. **Apply SAS congruence:** Triangles $\triangle ABE$ and $\triangle CDE$ have two pairs of congruent sides and the included angle congruent, so $\triangle ABE \cong \triangle CDE$ by SAS. **Final answer:** $\triangle ABE \cong \triangle CDE$.