What quadrilaterals have all sides parallel?

Answer 1

It's not possible to have all sides parallel.

The quadrilaterals that have every side parallel to the one opposite it ...

or two pairs of parallel sides ... are:

-- parallelograms

-- rhombera

-- rectangles

-- squares

Notice that

-- every square is also a rectangle, a rhombus, and a parallelogram.

-- every rectangle is also a parallelogram.

-- every rhombus is also a parallelogram.