Mathematics

In a parallelogram, the diagonals bisect each other—this is one of the defining properties that makes the shape so special. The key insight is to use the parallel sides and congruent triangles: since opposite sides are equal and parallel, triangles $AOB$ and $COD$ are congruent by SAS (they share vertical angles at $O$, and the parallel sides create equal alternate interior angles). From this congruence, the segments $AO$ and $OC$ must be equal.

In a parallelogram, the diagonals bisect each other—this is one of the defining properties that makes the shape so special. The key insight is to use the parallel sides and congruent triangles: since opposite sides are equal and parallel, triangles $AOB$ and $COD$ are congruent by SAS (they share vertical angles at $O$, and the parallel sides create equal alternate interior angles). From this congruence, the segments $AO$ and $OC$ must be equal.