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There is disagreement among authors on this. It depends on your definition of a trapezoid. A parallelogram is defined as a quadrilateral with opposite sides parallel. A trapezoid is defined as either
- a quadrilateral with at least one pair of parallel sides, or
- a quadrilateral with exactly one pair of parallel sides.
Therefore, if you go with the former definition, yes all parallelograms are trapezoids, because all parallelograms have at least one pair of parallel sides. If you use the latter definition, no.
The "at least one" definition is consistent with the trapezoid's uses in higher math, such as the trapezoidal rule for approximating integrals.
You can say, however, that all trapezoids are not parallelograms.
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Is All trapezoids parallelograms?
No trapezoids are parallelograms, and no parallelograms are trapezoids.
All trapezoids are parallelograms?
never
What is a quadrangle that has 2 pairs of equal sides but not a parallelogram?
Quadrangles that are not parallelograms = trapezoids, kites, any other polygon that is not a parallelogram
Are parallelograms and trapezoids always similar?
yes * * * * * Never. A parallelogram has two pairs of equal angles opposite one another. A trapezoid does not.
Why aren't trapezoids parallelograms?
Because a parallelogram is defined as having two pairs of parallel sides. A Trapezoid only has one pair.
