Existing models of galaxy formation have not yet explained striking correlations between structure and star formation activity in galaxies, notably the sloped and moving boundaries that divide star-forming from quenched galaxies in key structural diagrams. This paper uses these and other relations to "reverse engineer" the quenching process for central galaxies. The basic idea is that star-forming galaxies with larger radii (at a given stellar mass) have lower black hole (BH) masses due to lower central densities. Galaxies cross into the green valley when the cumulative effective energy radiated by their BH equals ∼4× their halo gas-binding energy. Because larger-radii galaxies have smaller BHs, one finds that they must evolve to higher stellar masses in order to meet this halo energy criterion, which explains the sloping boundaries. A possible cause of radii differences among star-forming galaxies is halo concentration. The evolutionary tracks of star-forming galaxies are nearly parallel to the green-valley boundaries, and it is mainly the sideways motions of these boundaries with cosmic time that cause galaxies to quench. BH scaling laws for star-forming, quenched, and green-valley galaxies are different, and most BH mass growth takes place in the green valley. Implications include the radii of star-forming galaxies are an important second parameter in shaping their BHs; BHs are connected to their halos but in different ways for star-forming, quenched, and green-valley galaxies; and the same BH-halo quenching mechanism has been in place since z ∼ 3. We conclude with a discussion of BH-galaxy coevolution and the origin and interpretation of BH scaling laws.