If you were to compare three stars with the same surface temperature, with one star being a giant, another a supergiant, and the third a main-sequence star, how would their radii compare to one another?

Radii of Super giant > giant > main sequence star.

Explanation:

A star becomes a giant after all the hydrogen available for fusion, in a main sequence star is depleted and its outer shell of the star expands.

Super giant and giant stars are very large in size compared to a main sequence star. For example, if a giant star has 20 times the diameter of main sequence star, the super giant's diameter is almost 300 times or even more than a main sequence star.  

Most of the stars are main sequence stars. After a star has spent a few million or even a few billion years as a main sequence star, it becomes a giant and a super giant star. These are the later stages of development of development of the main sequence star. Giant and super giant phase of a star's life is very short compared to the main sequence star.

they should be similar or the same

. west