Here is a link http://eprints.soton.ac.uk/41247/01/Fuj ... 0_2006.pdf
to a report on understanding of basic geometry amongst primary school teachers in Scotland.
The sad conclusion is that only 8.7% correctly knew that a square, a rectangle and a parallelogram are in fact all special cases of trapezia.
This contrast to 73% in Japan.
People are perhaps fooled by picture which show the general case (only one pair of parallel sides), and then think that special cases like a rectangle are not also examples of the more general trapezium.
Think of it as a hierarchy with the most special case (square) at the top, and more general cases going down.
Saying a parallelogram is not a trapezium is like saying a square is not a quadrilateral.
Unfortunately I'm not sure if all the examiners really understand the proper definitions either.
So the hierarchy is
Also a rhombus is a special case of a parallelogram.