Question

1. choose all answers that describe the polygon opqr if op = 11, pq = 11, qr = 11, ro = 11, m∠o = m∠q, and m∠p = m∠r.

parallelogram quadrilateral rectangle
rhombus square

Explanation:

Step1: Analyze the definition of quadrilateral

A quadrilateral is a polygon with four sides. Since \(OPQR\) has four sides \(OP\), \(PQ\), \(QR\), \(RO\), it is a quadrilateral.

Step2: Analyze the properties of parallelogram

In a parallelogram, opposite sides are equal and opposite angles are equal. Here, \(OP = QR = 11\), \(PQ=RO = 11\) (opposite sides equal) and \(\angle O=\angle Q\), \(\angle P=\angle R\) (opposite angles equal). So it is a parallelogram.

Step3: Analyze the properties of rhombus

A rhombus is a parallelogram with all sides equal. Since \(OP = PQ=QR = RO = 11\), it is a rhombus.

Step4: Analyze the properties of rectangle and square

For a rectangle, all angles should be \(90^{\circ}\). For a square, all angles should be \(90^{\circ}\) and all sides equal. We are not given that the angles are \(90^{\circ}\), so it is not a rectangle or a square.

Answer:

Parallelogram, Quadrilateral, Rhombus