1. **State the problem:** Given rhombus ABCD with AE \cong BE, prove ABCD is a square. 2. **Given:** ABCD is a rhombus and AE \cong BE. 3. **Step 1:** Since E lies on diagonal AC, and AE \cong BE, E is the midpoint of AC and BD. 4. **Step 2:** By definition of midpoint, AC = 2AE and BD = 2BE. 5. **Step 3:** Since AE \cong BE, then AC = 2AE = 2BE = BD, so AC \cong BD. 6. **Step 4:** A rhombus with congruent diagonals is a square. 7. **Step 5:** Therefore, ABCD is a square. 8. **Step 6:** Also, diagonals AC and BD bisect each other at E, confirming E is midpoint of both. **Final answer:** ABCD is a square because it is a rhombus with congruent diagonals that bisect each other.