A controversial "converse theorem"

First consider the theorem. This theorem is based on the assumption that

one of the parallels is the base of the triangle.

 

Fix this assumption that one of the parallels is the base of the triangle.

 

Now, consider the converse. In the diagram that you have provided, neither

of the two parallels is the base. Since it is violating the assumption,

the theorem cannot be applied to this situation.

 

The aim of the theorem is to show that if

            Area = (1/2) * Base * Height

and Base value and Area value are equal,

the Height value is also equal.

 

In the theorem, the Height value is presented as the distance between 2

parallel lines.

Due to the motive of the theorem, the Height value is thus,

the distance between the base and a line parallel to the base.