Final answer:
The quadrilateral described is a parallelogram, which is defined by having opposite sides parallel without requiring perpendicular diagonals or equal side lengths.
Step-by-step explanation:
If a quadrilateral has each of its sides parallel to its opposite side and the diagonals are not perpendicular, then the quadrilateral is a parallelogram. This is because one of the defining properties of a parallelogram is that opposite sides are parallel to each other. Although squares and rectangles are special types of parallelograms, they are characterized by having perpendicular diagonals, which is not the case according to the scenario provided. Similarly, a rhombus, which is also a parallelogram, does not fit if nothing is said about the sides being of equal length. Therefore, the most appropriate answer is a general parallelogram, which does not impose any additional conditions on the angles or the lengths of the sides and diagonals.