On what single issue does Atticus build his case?

Atticus questions Mr. Ewell, asking whether a doctor was called, and Mr. Ewell again says that no doctor was called, saying that he has never called a doctor in his life and never thought of doing so. Atticus asks if Mr. Ewell remembers Mayella's injuries as being the same as described by the sheriff. Mr. Ewell says that he does. Atticus asks if Mr. Ewell can write, and he says he can, so Atticus asks him to write his name on an envelope. In so doing, it is revealed that Mr. Ewell is left-handed. Mayella's injuries were inflicted upon her with the use of a "left" hand..... and as we find out, Tom's left hand was useless.