What shape does it have to be?

What does quadrilateral ABCD have to be even if any given point is moved on the shape?

What does quadrilateral EFGH have to be even if any given point is moved on the shape?

What does quadrilateral IJKL have to be even if any given point is moved on the shape?

What does quadrilateral MNOP have to be even if any given point is moved on the shape?

What does quadrilateral QRST have to be even if any given point is moved on the shape?