In this question, OA=OB is a necessary condition for our own parallelogram to become a rectangle: the diagonal lines of the rectangle are equal and equally divided.

Partial problem solving process

Let △OCD and △OAB be symmetric about the origin O.

The quadrilateral ABCD is a parallelogram.

When OA=OB, the parallelogram ABCD is rectangular.

Once again ∵=AO AB

△ OAB is an equilateral triangle

AE⊥OB, the vertical foot is e.