Final answer:
A counterexample to the conjecture that all quadrilaterals are rectangles can be a square, rhombus, or trapezoid, as each of these is a quadrilateral but does not possess all properties of a rectangle.
Step-by-step explanation:
A counterexample to the conjecture that all quadrilaterals are rectangles is any quadrilateral that is not a rectangle. For example, a square, rhombus, or trapezoid each have four sides, making them quadrilaterals, but none of these shapes share all the properties of a rectangle, which by definition has all angles equal to 90 degrees and opposite sides that are equal in length.
A square, while having all right angles, has all sides of equal length that makes it different from a rectangle. A rhombus has equal sides but does not generally have all angles at 90 degrees. A trapezoid has only one pair of parallel sides, which is also contrary to the properties of a rectangle.
Any of these shapes serve as a valid counterexample to prove that the conjecture is false because they are indeed quadrilaterals but not rectangles, which shows that not all quadrilaterals are rectangles.