In Chapter 15, Atticus is guarding the jail to protect Tom Robinson from a potential mob. The mob shows up, demanding Tom Robinson but Atticus refuses. Scout, Jem, and Dill have found Atticus at the jail and try to intervene. When Atticus tells Jem to take the children home, Jem refuses. Scout notes that Jem and Atticus do not resemble each other physically. But she adds that in attitude and determination, they do look similar:
As Atticus’s fists went to his hips, so did Jem’s, and as they faced each other I could see little resemblance between them: Jem’s soft brown hair and eyes, his oval face and snug-fitting ears were our mother’s, contrasting oddly with Atticus’s graying black hair and square-cut features, but they were somehow alike. Mutual defiance made them alike.
In Chapter 10, Atticus shoots and kills a rabid dog (Tim Johnson's dog). Up until this point, Scout and Jem have only viewed their father as an older man, never inclined to action. Seeing her father in action, Scout can't wait to brag about it. But Jem tells her not to, saying that Atticus would have told them if he wanted to brag about it. Jem learns that actions speak louder than words (bragging). He understands this is the mark of a gentleman, and he concludes that he wants to be like Atticus. In other words, he wants to resemble (in character) the way Atticus behaves:
Jem picked up a rock and threw it jubilantly at the carhouse. Running after it, he called back: “Atticus is a gentleman, just like me!”
While there is not much physical resemblance between the two, there are times when Jem tries to emulate his father in attitude and behavior.