Determine If the Quadrilateral is a Square: Analyzing Side and Angle Properties
Question
Look at the quadrilateral below.
Is the quadrilateral a square?
Step-by-Step Solution
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∘).
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 (∠A=∠B=∠C=∠D=90∘).
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∘.
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.