Trapezoids - Which definition has a stronger case? Today my daughter Ella asked me "Is a trapezoid an irregular polygon?" and I realized I cannot give her a definitive answer.
According to the Internet, trapezoids are alternately defined as having only one pair of parallel lines, and also at least one pair of parallel lines.  My understanding is that this is simply an unresolved ambiguity in mathematics.
My question is, which definition has the stronger case?  So far I have this:
The case for "only one":


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*Many people seem to think this is more intuitive and/or traditional


The case for "at least one":


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*Inclusive definitions are generally more useful (if this true I'd like to learn why)

*It's the only definition that fits with the concept of trapezoidal sums in calculus


What am I missing?

Short answer is that the definition being used should be explicitly spelled out in every context where it actually matters.

Inclusive definitions are generally more useful (if this true I'd like to learn why)

Take for example the area formula: if a quadrilateral has a pair of parallel sides, then its area is half the distance between the two parallels times the sum of those two sides.
The theorem obviously holds true for arbitrary trapezoids, but also for parallelograms, rhombi, rectangles and squares. If you defined each one in the strictest non-inclusive sense, then you would technically have to restate and/or prove the theorem separately for each shape in turn.
