Endosymbiosis and organelle evidence
Endosymbiotic theory explains mitochondria and chloroplasts as descendants of bacteria incorporated into ancestral host cells. Multiple lines of evidence support this account: genetic relationships with bacterial lineages, organelle genomes, bacterial-like translation machinery, division resembling binary fission, and surrounding membranes. No single superficial resemblance proves the theory by itself; converging evidence makes the inference strong. Many ancestral organelle genes have been lost or transferred to the nucleus, and modern organelles depend on numerous nuclear-encoded proteins. They are integrated parts of eukaryotic cells rather than fully independent bacteria living unchanged inside them.
A chloroplast gene sequence groups with cyanobacterial homologs in a well-supported phylogeny. Combined with its own DNA and bacterial-like ribosomes, that relationship supports shared ancestry more strongly than green color alone would.
The nucleus is not explained by the classic mitochondrial/chloroplast endosymbiosis evidence. Also, an organelle having some DNA does not mean it can survive independently.