Detailed definition
Understanding Trapezoid
Trapezoid is a quadrilateral with at least one pair of parallel sides. A trapezoid has at least one pair of parallel sides. In the usual U.S. definition, the parallel sides are called the bases and the non-parallel sides are called the legs.
That wording matters because some sources use an exclusive definition requiring exactly one pair of parallel sides. This page follows the inclusive school-geometry definition stated in the catalog.
A trapezoid is useful because it sits between general quadrilateral classification and more specific forms such as the isosceles trapezoid. It also introduces base, height, and median language that reappears in area work.
Key facts
Important ideas to remember
- A trapezoid has at least one pair of parallel sides.
- The parallel sides of a trapezoid are its bases.
- The legs are the non-parallel sides in the standard picture.
- If a quadrilateral has two pairs of parallel sides, it becomes a parallelogram.
Where it is used
Where trapezoid shows up
- Use trapezoid structure in area and median problems involving parallel bases.
- Use it when sorting quadrilaterals by the number of parallel-side pairs.
- Use it in coordinate geometry when testing whether one pair of sides remains parallel.
Common mistakes
What to watch out for
- Do not ignore the definition being used; textbooks differ on whether trapezoid means at least one or exactly one pair of parallel sides.
- Do not confuse the bases with the legs when setting up area or median reasoning.
- Do not assume a quadrilateral is a trapezoid only because one pair of sides looks nearly parallel.