Trapezoids: just the answers:

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.

If you thought only a and b or only a were trapezoids, then you are probably think of a trapezoid as something that looks like a red pattern block (the standard picture of a trapezoid), rather than thinking about trapezoids in terms of their properties.

2. The defining property of a trapezoid (U.S. definition) is that it is a quadrilateral with exactly one pair of parallel sides (one and only one). If you prefer the Canadian definition, then you would say that it is a quadrilateral with at least one pair of parallel sides. This information is enough to tell if something is a trapezoid or not.

There are also other properties of trapezoids that are true, such as that it is convex, and that at least one pair of opposite sides have different lengths (US defn.), and the quadrilateral conditions may be explained: it is closed, and all of the sides are straight.

3. The correct answer (when working with the U.S. definition) is a because you can never have a parallelogram that is a trapezoid and vice versa. If you are working with the Canadian definitition , then you should have chosen c, which shows that parallelograms are special kinds of trapezoids.