Geometry

Question Analysis:
This question tests the fundamental theorem that diagonal bisection is both necessary and sufficient to prove a quadrilateral is a parallelogram.

Key Concept Explanation:
The defining property of parallelograms regarding diagonals states: If both diagonals bisect each other (each is divided into two equal parts at intersection), the quadrilateral must be a parallelogram.
This is a two-way conditional relationship.

Step-by-Step Solution:
The condition requires both diagonals to be bisected (AO = OC AND BO = OD).
Single diagonal bisection (A or B alone) could occur in other quadrilaterals like kites.
Equal diagonal length (D) is irrelevant for proving paralle...