1. **State the problem:** Given that ABCD is a rhombus, prove that triangles $\triangle AEB$ and $\triangle CEB$ are congruent. 2. **Step 1:** Statement: ABCD is a rhombus. Reason: Given. 3. **Step 2:** Statement: $\overline{AE} \cong \overline{EC}$. Reason: The diagonals of a rhombus bisect each other, so point E is the midpoint of diagonal AC. 4. **Step 3:** Statement: $\overline{AE} \cong \overline{EC}$. Reason: A segment bisector divides a segment into two congruent segments. 5. **Step 4:** Statement: $\overline{AB} \cong \overline{BC}$. Reason: All sides of a rhombus are congruent. 6. **Step 5:** Statement: $\overline{BE} \cong \overline{BE}$. Reason: Reflexive Property (a segment is congruent to itself). 7. **Step 6:** Statement: $\triangle AEB \cong \triangle CEB$. Reason: By the Side-Side-Side (SSS) congruence postulate, since all three corresponding sides are congruent. **Final conclusion:** Triangles $\triangle AEB$ and $\triangle CEB$ are congruent by SSS congruence.