Question Choose ALL answers that describe the polygon \( S T U V \) if \( S T=12, T U=12, U V=12 \), \( V S=12, \mathrm{~m} \angle S=\mathrm{m} \angle U \), and \( \mathrm{m} \angle T=\mathrm{m} \angle V \). Answer Atemptiout of 2 Parallelogramples Quadrilateral Rectangle Rhombus Square Trapezoid

To analyze the polygon \( S T U V \) based on the given conditions, let's break down the information step by step: 1. **Sides of the Polygon**: - We know that \( S T = 12 \), \( T U = 12 \), \( U V = 12 \), and \( V S = 12 \). This means all sides of the polygon are equal, indicating that it is a rhombus or a square. 2. **Angles of the Polygon**: - The conditions state that \( \mathrm{m} \angle S = \mathrm{m} \angle U \) and \( \mathrm{m} \angle T = \mathrm{m} \angle V \). This suggests that the opposite angles are equal. 3. **Types of Quadrilaterals**: - A **parallelogram** has opposite sides that are equal and opposite angles that are equal. - A **rectangle** has all angles equal to \( 90^\circ \) and opposite sides equal. - A **rhombus** has all sides equal and opposite angles equal. - A **square** is a special case of both a rectangle and a rhombus, where all sides are equal and all angles are \( 90^\circ \). - A **trapezoid** has at least one pair of parallel sides, which is not indicated here. 4. **Conclusion**: - Since all sides are equal and opposite angles are equal, \( S T U V \) is at least a rhombus. - If the angles \( \mathrm{m} \angle S \) and \( \mathrm{m} \angle T \) are \( 90^\circ \), then it would also be a rectangle and thus a square. However, we do not have information confirming that the angles are \( 90^\circ \). Based on this analysis, the polygon \( S T U V \) can be classified as: - **Rhombus** (since all sides are equal and opposite angles are equal) - **Quadrilateral** (since it has four sides) The other options (parallelogram, rectangle, square, and trapezoid) cannot be definitively concluded without additional information about the angles. ### Final Answers: - Rhombus - Quadrilateral