A fairly simple piece of evidence for the endosymbiotic hypothesis is the fact that both mitochondria and chloroplasts have double phospholipid bilayers. This appears to have arisen by mitochondria and chloroplasts entering eukaryotic cells via endocytosis. Both purple, aerobic bacteria (similar to mitochondria) and photosynthetic bacteria (similar to chloroplasts) only have one phospholipid bilayer, but when they enter another cell via endocytosis, they are bound by a vesicle which forms the second layer of their double phospholipid bilayer.
MISCONCEPTION: Science can only disprove ideas. CORRECTION: This misconception is based on the idea of falsification, philosopher Karl Popper's influential account of scientific justification, which suggests that all science can do is reject, or falsify, hypotheses that science cannot find evidence that supports one idea over others. Falsification was a popular philosophical doctrine especially with scientists but it was soon recognized that falsification wasn't a very complete or accurate picture of how scientific knowledge is built. In science, ideas can never be completely proved or completely disproved. Instead, science accepts or rejects ideas based on supporting and refuting evidence, and may revise those conclusions if warranted by new evidence or perspectives.