Analyzing Quadrilateral ABCD: Is It a Square Based on Its Properties?

To determine whether quadrilateral $ABCD$ is a square, we need to check two main properties:

• All four sides must be of equal length.
• All angles must be $90^\circ$.

In the context of the given geometrical figure, even though the diagram appears as a quadrilateral within a square shape, the internal details such as equal side lengths and angle measures are not specified or labeled.

Without confirmation of equal side lengths and precise angle measurements from the problem, we cannot definitively classify $ABCD$ as a square based solely on appearance. For a definitive determination, specific geometric calculations or measurements are required.

Therefore, $ABCD$ is not a square, without concrete evidence supporting the properties of a square.

The correct answer to the problem is no.