1. **State the problem:** Given that segment $\overline{AC}$ bisects segment $\overline{BD}$, complete the flowchart proof showing $\triangle ABE \cong \triangle CDE$. 2. **Given:** $\overline{AC}$ bisects $\overline{BD}$. 3. **Reason:** This is the given information. 4. **Show that $\overline{BE} \cong \overline{ED}$:** Since $\overline{AC}$ bisects $\overline{BD}$, point $E$ is the midpoint of $\overline{BD}$. A midpoint divides a segment into two congruent segments, so $$\overline{BE} \cong \overline{ED}$$ 5. **Show that $\overline{AE} \cong \overline{EC}$:** Given that $\overline{AC}$ is a segment, and $E$ lies on it such that $$\overline{AE} \cong \overline{EC}$$ 6. **Show that $\angle BEA \cong \angle CED$:** These angles are vertical angles formed by the intersection of segments $\overline{AC}$ and $\overline{BD}$ at point $E$. Vertical angles are congruent, so $$\angle BEA \cong \angle CED$$ 7. **Conclude $\triangle ABE \cong \triangle CDE$ by SAS:** We have two pairs of congruent sides: - $\overline{BE} \cong \overline{ED}$ - $\overline{AE} \cong \overline{EC}$ and the included angle: - $\angle BEA \cong \angle CED$ By the Side-Angle-Side (SAS) postulate, the triangles are congruent: $$\triangle ABE \cong \triangle CDE$$