Parallelograms which are on the same base and in the same parallels equal one another.

Is this proposition true if the parallelograms in question is a square?

Let ABCD be a square, and from base cd, let another parallelograms be created. Let's call the new parallelograms EBCF. Since it's a parallelograms, EF is equal to BC.

According to Euclid, the square ABCD is equal to EBCF. And here is my problem: how can they be equal? Unless drawn on the same side, EBCF will have two diagonals which will be more than the bases. EBCF will not be a square, how can it be equal to ABCD?