Based on examples she has seen, a child might think that a trapezoid is" a shape with 4 sides, top and bottom are parallel, bottom longer than the top, no sides the same size, large, no right angles, cut off at the top." Which of these characteristics are relevant?

To determine which characteristics are relevant in defining a trapezoid, we can refer to the actual definition of a trapezoid.

A trapezoid is a quadrilateral with exactly one pair of parallel sides. Based on this definition, let's evaluate the characteristics provided:

1. Shape with 4 sides: This is relevant as it aligns with the definition of a quadrilateral.
2. Top and bottom are parallel: This is relevant and essential since a trapezoid must have one pair of parallel sides.
3. Bottom longer than the top: This characteristic is relevant because it corresponds to the definition of a trapezoid, where the parallel sides have different lengths.
4. No sides the same size: This characteristic is not necessarily relevant to defining a trapezoid. Sides can be of different lengths, but they can still be the same if the top and bottom sides are equal.
5. Large: The size of the trapezoid is not relevant to its definition. It can be large or small.
6. No right angles: This characteristic is not relevant to defining a trapezoid. A trapezoid can have right angles if it is an isosceles trapezoid, where the non-parallel sides are equal in length.
7. Cut off at the top: The shape being cut off at the top is not relevant to defining a trapezoid.

In summary, the relevant characteristics for defining a trapezoid are: having 4 sides, top and bottom being parallel, and the bottom side being longer than the top side.