Explain the endosymbiotic theory

It is thought that it happened at least two times. The first time, an anaerobic organism took in an aerobic bacterium. The smaller, aerobic cell existed inside a vesicle in the cytoplasm of the larger cell, and reproduced at the same rate. Eventually, the bacterium turned into mitochondria and the larger cell into a heterotrophic eukaryote (animal). Then the second time, a heterotrophic cell took in a photosynthetic bacterium, and eventually the bacterium turned into chloroplasts and the larger cell into an autotrophic plant. Chloroplasts and mitochondria are very alike prokaryotes; both have 70s ribosomes to synthesize their own proteins, they reproduce like cells, they have naked circular DNA, and a double membrane which is what you would expect when a cell is taken in as a vesicle