1. The problem states that the dashed line is perpendicular to line segment AB and passes through point E. 2. If AE \cong BE, it means point E is the midpoint of segment AB. 3. A perpendicular bisector of a segment is a line that is perpendicular to the segment and passes through its midpoint. 4. Since the dashed line is perpendicular to AB and passes through E, if AE \cong BE, then the dashed line is indeed the perpendicular bisector of AB. 5. Therefore, the statement "If AE \cong BE, then the dashed line is perpendicular bisector of AB" is true.