How does Atticus show that Tom Robinson could not committed the crime he was accused of?

There was a lot of evidence that Atticus produces that proved Tom Robinson did not commit the crime. Perhaps the most persuasive evidence was that, according to the sheriff's testimony, Mayella's bruises were on the right side of her face, which means she was most likely punched with a left hand. Tom Robinson's left arm is useless due to an old accident, whereas Mr. Ewell leads with his left. Unfortunately, the jury had decided that Tom Robinson was guilty well before the trial started.