Determine If the Quadrilateral is a Square: Analyzing Side and Angle Properties

Look at the quadrilateral below.

Is the quadrilateral a square?

To determine if the quadrilateral is a square, we need to verify the defining characteristics of a square:

• All four sides must be of equal length.
• Each of the four angles must be a right angle ($90^\circ$).
• The diagonals should be equal and bisect each other at right angles.

From the problem description and the diagram provided:

• The quadrilateral is labeled ABCD, and the diagram shows right angles at each corner ($\angle A = \angle B = \angle C = \angle D = 90^\circ$).
• Visual inspection of the diagram suggests the sides AB, BC, CD, and DA appear equal, conforming to the property that all sides of a square are equal. This is inferred based on the symmetry and right angles in the diagram.
• Furthermore, the diagonals AC and BD in the diagram intersect at right angles, suggesting they are equal and bisect each other, which is a characteristic property of a square.

Therefore, checking all the conditions:

• Equal sides — based on the diagram.
• Right angles at each vertex — confirmed as all angles are labeled $90^\circ$.
• Equal and bisected diagonals — inferred from the intersection and right angles.

Conclusively, the quadrilateral satisfies all the characteristics of a square. Thus, the given quadrilateral is indeed a square.

Yes, the shape is a square.