In fig i, parallelogram ABCD and trapezium ABFE have a common base AB but they are not in between the same parallels. In figure ii, parallelogram ABCD and ABEF are on the same base AB and in between the same parallels (AB / DE).

In fact, two figure are said to be on the same base and in between the same parallels if they have common base and the vertices (vertex) opposite to the common base of each figure lie on a line parallel to the base.