Why can't I know if the figure is a rectangle, if angles c+d=180 and c=d?

Question

I have a four sided figure, abcd (see the image, and ignore the EF part), where I know that angles c+d=180 and c=d.

However, this isn't enough information to decide if this is a rectangle - why is that?

Answer 1

Here...we have made two parallel lines AD and BC;where CD is the shortest distance between those parallel lines Hence,c and d both being 90 degrees; but we cannot say it is a rectangle until and unless we are not sure that even AB is the shortest distance...if AB is not the shortest distance...it will form a trapezium

Answer 2

Using euclidean geometry only, it is easy to find a figure which attends the given properties (4 sides with two adjacent angles which are equal and whose sum equals 180º).

Take a right trapezium for instance, it has all of the aforementioned properties yet it is not a rectangle.

Trapezium