Question

choose all answers that describe the quadrilateral rstu if rs = 31, st = 33, tu = 35, ur = 45, m∠r = 59°, m∠s = 135°, m∠t = 72°, and m∠u = 94°. answer attempt 1 out of 2 parallelogram quadrilateral rectangle rhombus square trapezoid

Explanation:

• A quadrilateral is a four - sided polygon. Since \(RSTU\) has four sides, it is a quadrilateral.
• For a parallelogram, opposite sides are equal and parallel and opposite angles are equal. Here, \(RS = 31\), \(ST=33\), \(TU = 35\), \(UR = 45\) (sides are not equal in pairs) and \(m\angle R=59^{\circ}\), \(m\angle S = 135^{\circ}\), \(m\angle T=72^{\circ}\), \(m\angle U = 94^{\circ}\) (angles are not equal in pairs). So it is not a parallelogram.
• A rectangle is a parallelogram with all angles equal to \(90^{\circ}\). Since angles are \(59^{\circ},135^{\circ},72^{\circ},94^{\circ}\), it is not a rectangle.
• A rhombus is a parallelogram with all sides equal. Since sides are \(31,33,35,45\) (not equal), it is not a rhombus.
• A square is a rectangle and a rhombus (all sides equal and all angles \(90^{\circ}\)). Since it is neither a rectangle nor a rhombus, it is not a square.
• A trapezoid is a quadrilateral with at least one pair of parallel sides. There is no information given about parallel sides, but the most basic classification is that it is a quadrilateral.

Answer:

Quadrilateral