Vidqun....
As with all evidence for common ancestry and evolution there are many strands of evidence which come together to create a strong case for the emergence of eukaryotes.
The evidence that supports the theory that eukaryotic cells are the descendants of separate prokaryotic cells that combined by invagination resulting in a symbiotic union rest primarily with their physiology and structure. It specifically centres around physiology and structure of two specific organelles, mitochondria and chloroplasts which are similar in size and morphology to ancient bacterial prokaryotic cells.
Mitochondria and chloroplasts are clones of pre-existing mitochondria and chloroplasts reproducing by a type of asexual reproduction called binary fission, this a prokaryote bacterial trait and not the eukaryotic method (mitosis). Why would two systems of reproduction occur within a single cell unless these organelles have a different ancestry from the nucleus?
The membranes of the chloroplasts and mitochondria have different chemistries within their membrane systems. Mitochondria and chloroplasts possess a double membrane the outer membrane corresponds to the membranes found in prokaryotic bacteria whereas the inner membrane’s chemistry is of a different chemical composition very similar to that of eukaryotic bacteria.
In these organelles the enzymes and inner membrane systems resemble prokaryotic inner membrane systems whereas outer membrane is of similar composition to the plasma membrane, and other organelles such as the endoplasmic reticulum or nuclear membrane of the eukaryote. These chemical mismatches are most readily explained by the theory that prokaryotes were absorbed and formed a symbiotic relationship.
Finally mitochondria and chloroplasts have their own DNA resembling that of bacterial prokaryotic cells and they also possess their own ribosomes which also resemble bacterial prokaryotic cells: The DNA of mitochondria and chloroplasts is different from that of the eukaryotic cell in which they are found. Both types of organelle include circular, not linear DNA, a characteristic of prokaryotes.