Which of the following quadrilaterals has all sides equal and all angles equal?

The correct answer is the square, which is a specific type of quadrilateral that possesses both equal sides and equal angles. In a square, all four sides are of equal length, and each of the interior angles measures 90 degrees. This unique combination of properties distinguishes the square from other quadrilaterals.

In contrast, although a rectangle has all angles equal to 90 degrees, its sides are not necessarily of equal length. A rhombus, while it does have all sides equal, does not have the requirement that all angles be equal; typically, opposite angles are equal, and adjacent angles are supplementary. Lastly, a trapezoid does not meet either condition, as it has only one pair of parallel sides and can have various side lengths and angles. Thus, the square remains the only quadrilateral from the choices provided that is characterized by both all sides being equal and all angles being equal.