Question

question
choose all answers that describe the polygon qrst if qr = rs = st = tq,
m∠q = 90°, m∠r = 90°, m∠s = 90°, and m∠t = 90°.
answer attempt 1 out of 2
parallelogram
quadrilateral
rectangle
rhombus
square
trapezoid

Explanation:

Step1: Analyze the properties of each quadrilateral

• Quadrilateral: A four - sided polygon. Since \(QRST\) has four sides (\(QR = RS=ST=TQ\) and four angles \(\angle Q=\angle R=\angle S=\angle T = 90^{\circ}\)), it is a quadrilateral.
• Parallelogram: A parallelogram has opposite sides equal and parallel. Here, \(QR = ST\), \(RS=TQ\) (given \(QR = RS=ST=TQ\)) and opposite angles are equal (all angles are \(90^{\circ}\)). So it is a parallelogram.
• Rectangle: A rectangle is a parallelogram with all angles equal to \(90^{\circ}\). Since \(QRST\) is a parallelogram (\(QR = ST\), \(RS=TQ\)) and \(\angle Q=\angle R=\angle S=\angle T = 90^{\circ}\), it is a rectangle.
• Rhombus: A rhombus is a parallelogram with all sides equal. Since \(QR = RS=ST=TQ\) and it is a parallelogram, it is a rhombus.
• Square: A square is a parallelogram with all sides equal and all angles equal to \(90^{\circ}\). Since \(QR = RS=ST=TQ\) and \(\angle Q=\angle R=\angle S=\angle T = 90^{\circ}\), it is a square.
• Trapezoid: A trapezoid has at least one pair of parallel sides. But a trapezoid does not necessarily have all sides equal and all angles equal to \(90^{\circ}\). Since \(QRST\) has more properties (all sides equal and all angles \(90^{\circ}\)), it is not just a trapezoid.

Answer:

Square, Rhombus, Rectangle, Parallelogram, Quadrilateral