1. **Problem Statement:** We are given a quadrilateral STUV with the following properties: - $ST \cong UV$ - $TU \cong VS$ - $m\angle S = m\angle T = m\angle U = m\angle V$ We need to identify all possible classifications of this polygon. 2. **Understanding the properties:** - Since $ST \cong UV$ and $TU \cong VS$, opposite sides are congruent. - All interior angles are equal, so $m\angle S = m\angle T = m\angle U = m\angle V = 90^\circ$ because the sum of interior angles in a quadrilateral is $360^\circ$ and equal angles imply each angle is $\frac{360^\circ}{4} = 90^\circ$. 3. **Implications:** - Opposite sides congruent and all angles $90^\circ$ means the quadrilateral is a rectangle. - Since opposite sides are congruent but not necessarily all sides equal, it may or may not be a rhombus. - A rhombus requires all sides equal, which is not given. - A square requires all sides equal and all angles $90^\circ$, which is not guaranteed here. - A parallelogram requires opposite sides parallel and equal, which is true here. - A quadrilateral is any four-sided polygon, so it is always true. 4. **Conclusion:** - The polygon STUV is a parallelogram (opposite sides congruent). - It is a rectangle (all angles $90^\circ$). - It is a quadrilateral (four-sided polygon). - It is not necessarily a rhombus or square because all sides equal is not given. **Final answers:** Parallelogram, Quadrilateral, Rectangle.