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Trapezoids are not considered parallelograms because parallelograms have 2 pairs of parallel sides, whereas trapezoids have only one.

Some definitions of trapezoid say "at least one pair of parallel sides" in which case, some trapezoids would be parallelograms (the ones that have 2 pairs of parallel sides), but most textbooks in the US now define trapezoids as "exactly one pair of parallel sides."

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Q: Why are trapezoids outside the parallelogram?
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