How could scientists produce accurate chemical structures before they could capture images of molecules? How were scientists able to produce these accurate structural diagrams long before scientists were able to capture images of the actual molecules?

Reference: Scientists capture first images of molecules before and after reaction
They ran chemical reactions on the molecule and identified the fragments.  Then like a jigsaw puzzle, using additional information derived from other chemical reactions, they pieced the molecule back together.  Some Nobel prizes were awarded for such structure determinations.