a quadrilateral has opposite sides that are parallel and diagonals which bisect each other, which of the following shapes ould the quadrilateral be? Rhombus I. Trepezoid II. Square N. Rectangle I, II, III only I, m, N only II only III only

A quadrilateral that has opposite sides parallel and diagonals that bisect each other is specifically a parallelogram. This means it could indeed be a rhombus, rectangle, or square, as all three shapes fit these criteria. In the realm of geometry, parallelograms are like the “family” of shapes where each member possesses unique attributes while sharing key characteristics. When approaching problems like this, it's important to visualize. Drawing the shapes helps identify their properties. Common mistakes include overlooking that while all squares and rhombuses are parallelograms (and thus have the described properties), not all parallelograms are squares or rhombuses—rectangles could also fit the description. So always sketch before finalizing your answer!