Trapezoids answers, with a discussion of Van Heile levels of understanding:

Problem 1. By the definition that is usually used in the United States, a-d are trapezoids. If you thought that all of the figures were trapezoids, then you have probably internalized the Canadian definition of trapezoid. Either of these responses indicates a probable (at least) level 1 understanding (analysis). If you thought only a and b or only a were trapezoids, then your notion of trapezoid is governed largely by the example of the standard pattern-block isosceles trapezoid, and you are probably at a level 0 understanding of trapezoid (visualization).

2. The defining characteristic of a trapezoid (U.S. definition) is that it is a quadrilateral with exactly one pair of parallel sides. If you prefer the Canadian definition, then you would say that it is a quadrilateral with at least one pair of parallel sides. Other characteristics may be added, such as that it is convex, and that at least one pair of opposite sides have different lengths (US defn.), or the quadrilateral conditions may be explained: it is closed, and all of the sides are straight. If your response distinguishes between the defining characteristics (one pair of parallel sides), and the characteristics which are a result of the definition (being convex, or side length properties), then you may have a level 2 understanding (abstraction). If your response does not distinguish between these, and you are not sure why some properties are more important than others, then you probably have a level 1 understanding.

3. The correct answer (when working with the U.S. definition) is a. If you are working with the Canadian definitition , then you should have chosen c. If you made a correct choice that was consistent with the answers you gave to #1 and 2 (U.S. or Canadian), and you can imagine example figures you could use to explain each section of the diagram, then you are probably at Van Hiele level 2 with respect to the concept of trapezoids. If you made another choice: a choice that was inconsistent with your previous answers then you are probably at a level lower than 2 with respect to the concept of a trapezoid.