In To Kill a Mockingbird, what are the main points in Heck Tate's evidence, and what does Atticus show in his cross examinaion of Sheriff Tate?

Heck Tate testifies first that Mayella was not examined by a doctor. He then testifies that she had been beaten mostly around her head and that "she had a black eye comin'." Atticus' questions lead Heck to realize that it was Mayella's right eye that had been injured and that most of the injuries to her head occurred on the right side. This is enormously significant because Heck's testimony establishes that Mayella's injuries would have been inflicted by a left-handed person.

Atticus understands the importance of Heck's testimony. When Bob Ewell testifies after Heck Tate, Atticus establishes clearly that Ewell is left-handed. Atticus later establishes that Tom Robinson's left arm is crippled, making his left hand useless. Because of Heck's testimony, it becomes very clear that Bob Ewell most likely attacked Mayella, and that Tom Robinson could not have inflicted the injuries to her head and right eye.