Question

answer attempt 1 out of 2
choose all answers that describe the quadrilateral below.
parallelogram
rectangle
rhombus
square
trapezoid

Explanation:

Step1: Recall properties of parallelogram

A parallelogram has opposite sides equal and parallel. But here, diagonals are perpendicular (\(x\perp s\)) and bisect each other (segments of diagonals are equal).

Step2: Recall properties of rhombus

A rhombus is a parallelogram with all sides equal and diagonals perpendicular bisectors of each other.

Step3: Recall properties of square

A square is a special rhombus with all angles \(90^{\circ}\). But we are not given angle information. However, since diagonals are perpendicular bisectors (a property of rhombus and square), and all sides of a square are equal (also true for rhombus, but square has right - angles which is not indicated here). But since square is a type of rhombus.

Step4: Recall properties of trapezoid, rectangle

A trapezoid has only one pair of parallel sides. A rectangle has diagonals equal in length and not necessarily perpendicular (unless it is a square).

Answer:

Square, Rhombus