Final answer:
Mitochondria and chloroplasts having their own DNA, ribosomes similar to those found in bacteria, and a double membrane structure provides evidence for their endosymbiotic origins.
Step-by-step explanation:
The feature of mitochondria and chloroplasts that provides evidence for their endosymbiotic origins is that they both have their own DNA. This is significant because their DNA is similar to that of prokaryotic cells, specifically bacteria. Additionally, the presence of ribosomes within these organelles that resemble bacterial ribosomes, and the method of replication through binary fission which is similar to bacteria, provides further evidence of an endosymbiotic origin. The double-membrane structure of these organelles is also indicative of an endosymbiotic event, with the theory being that one membrane comes from the engulfed bacteria and the second from the host eukaryotic cell.