Characterizations
A convex quadrilateral is a trapezoid if and only if it has two adjacent angles that are supplementary, that is, they add up 180 degrees.
Another necessary and sufficient condition is that the diagonals cut each other in mutually the same ratio (this ratio is the same as that between the lengths of the parallel sides).
A convex quadrilateral is also a trapezoid if and only if the diagonals cut the quadrilateral into four triangles of which one opposite pair are similar.
Read more about this topic: Trapezoid