A parallelogram is a figure with four straight sides whose opposite sides are parallel and equal in length and whose opposite angles are equal. A trapezoid is also a figure with four straight sides. However, only one pair of opposite sides is parallel. A trapezoid does not have opposite sides that are equal in length, and many times, all angles are different.
The parallel sides of a trapezoid are called bases, and the other sides are called legs. Both parallelograms and trapezoids fall under the general category of quadrilaterals. Quadrilaterals include all two-dimensional figures with four straight sides whose interior angles add up to 360 degrees. Other examples of quadrilaterals include the square, rectangle, rhombus and kite. Squares, rectangles and rhombuses also fit the definition of a parallelogram.
Trapezoids are considered isosceles trapezoids if the legs are equal in length and both angles coming from the bases are equal. In the United Kingdom, a trapezoid is called a trapezium. In the United States, a trapezium is defined as a quadrilateral with no parallel sides, whereas the United Kingdom uses this definition for a trapezoid. Basically, the United Kingdom's definitions for trapezium and trapezoid are exactly opposite of the United States' definitions.