Final answer:
If one diagonal of a parallelogram bisects a pair of opposite angles, then the parallelogram is a rhombus.
Step-by-step explanation:
In order to prove that if one diagonal of a parallelogram bisects a pair of opposite angles, then the parallelogram is a rhombus, we can use the properties of a rhombus. A rhombus is a quadrilateral with all sides of equal length. If one diagonal of a parallelogram bisects a pair of opposite angles, it creates congruent triangles. These congruent triangles have equal side lengths and equal angles, which means the opposite sides of the parallelogram are equal in length. Therefore, the parallelogram is a rhombus.