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.
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.
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