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For the same reason that a cat is an animal but an animal is not always a cat.

Because a trapezoid is a special kind of quadrilateral.

A quadrilateral is anything with four sides.

A trapezoid has four sides, and also two of them are parallel to each other.

Therefore some quadrilaterals are trapezoids, but most of them aren't.

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Q: Why is a trapezoid a quadrilateral but a quadrilateral is not a trapezoid?
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