Consider the following figure, which shows two parallelograms ABCD and ABEF on the same base AB:

Parallelograms with same base

Here’s another example. In the following figure, parallelogram ABCD and triangle ABE are on the same base AB:

Parallelogram and triangle with same base

Now, consider the following figure, in which two parallelograms ABCD and ABEF are on the same base as well as between the same parallels:

Parallelograms - same base same parallels

Finally, consider the following figure, in which parallelogram ABCD and triangle ABE are on the same base as well as between the same parallels:

Parallelogram and triangle - same base same parallels

We see that two figures can be said to be on the same base and between the same parallels if they have a common base (a common side) and the vertex (or vertices) opposite to the common base of each figure lie on some line parallel to the base.

In the following figure, the two triangles are on the same base but not between the same parallels:

Triangles - same base not parallels