Use the properties of quadrilaterals to determine the quadrilaterals that can be constructed with opposite congruent sides but with diagonals that do not bisect opposite angles.
A quadrilateral with opposite congruent sides is a parallelogram. If a parallelogram has diagonals that do not bisect opposite angles, it must be a rhombus.
A rhombus is a quadrilateral with all sides congruent, opposite sides parallel, and diagonals that bisect each other at right angles. Therefore, a rhombus is a quadrilateral with opposite congruent sides but with diagonals that do not bisect opposite angles.