1. The problem asks to explain what a perpendicular line segment in a rhombus is, including its shape and examples. 2. A rhombus is a quadrilateral with all sides equal in length. Its opposite sides are parallel, and opposite angles are equal. 3. A perpendicular line segment in a rhombus is a segment that intersects another segment at a right angle ($90^\circ$). 4. In a rhombus, the diagonals are special because they are perpendicular to each other. This means the diagonals intersect at right angles. 5. For example, if the rhombus has vertices $A$, $B$, $C$, and $D$, then the diagonals $AC$ and $BD$ intersect at point $O$ such that $$AC \perp BD$$ and $\angle AOB = \angle BOC = \angle COD = \angle DOA = 90^\circ$. 6. This property is unique to rhombuses among parallelograms, as not all parallelograms have perpendicular diagonals. 7. To summarize, a perpendicular line segment in a rhombus is typically one of the diagonals intersecting the other diagonal at a right angle, dividing the rhombus into four right triangles. Final answer: The diagonals of a rhombus are perpendicular line segments intersecting at right angles.