1. The problem asks about the perpendicular line segment in a rhombus. 2. A rhombus is a quadrilateral with all sides equal in length. 3. The perpendicular line segment in a rhombus usually refers to the segment formed by the intersection of its diagonals. 4. The diagonals of a rhombus are perpendicular to each other, meaning they intersect at a right angle ($90^\circ$). 5. This perpendicular intersection divides the rhombus into four right triangles. 6. The length of the perpendicular segment is the length of one diagonal, and the other diagonal is also perpendicular to it. 7. Therefore, the perpendicular line segment in a rhombus is the segment where the diagonals intersect at right angles. 8. This property is unique to rhombuses among parallelograms. Final answer: The perpendicular line segment in a rhombus is the segment formed by the intersection of its diagonals, which are perpendicular to each other.