8. Multiple Choice Which is a counterexample to the conjecture, "If a quadrilateral is equiangular, then it is equilateral"? \( \begin{array}{ll}\text { A A rectangle that is not a rhombus } & \text { B A rhombus that is not rectangular } \\ \text { C Any square } & \text { D Any parallelogram }\end{array} \)

To determine which option serves as a counterexample to the conjecture "If a quadrilateral is equiangular, then it is equilateral," we need to understand the definitions involved: - An **equiangular quadrilateral** has all angles equal (each angle is 90 degrees for rectangles, for example). - An **equilateral quadrilateral** has all sides of equal length (like a rhombus or a square). Now, let's analyze the options: - **A. A rectangle that is not a rhombus**: A rectangle has all angles equal (90 degrees) but does not necessarily have all sides equal (the sides can be of different lengths). This is a counterexample because it is equiangular but not equilateral. - **B. A rhombus that is not rectangular**: A rhombus has all sides equal but does not necessarily have all angles equal (the angles can be different). This does not serve as a counterexample because it is equilateral but not equiangular. - **C. Any square**: A square is both equiangular and equilateral. This does not serve as a counterexample. - **D. Any parallelogram**: A parallelogram has opposite angles equal but not necessarily all angles equal. This does not serve as a counterexample because it does not guarantee equiangularity. The correct answer is **A. A rectangle that is not a rhombus**.