Atticus's shooting of the rabid dog in Chapter 10 is symbolic for several reasons. First, it is proof to his children that he is not the "feeble" father they had first imagined earlier in the chapter. Atticus's secret is a sign of his humble nature, and it is the first lesson in humility that he teaches his children. In the following chapter, Atticus is quick to point out that his style of courage--"a man with a gun in his hand"--is not the same as Mrs. Dubose's fight against morphine addiction. She was, Atticus tells his children, "the bravest person I ever knew."
But as the jury returns to the courtroom, the scene has "a dreamlike quality" to Scout as she flashes back to the image of Atticus standing alone on the street, facing the dog with a rifle in his hand. This time, however, Atticus had run out of ammunition, and as Judge Taylor's "tiny" voice seemingly "came from far away,"
... it was like watching Atticus walk into the street, raise a rifle and pull the trigger, but watching all the time knowing that the gun was empty.
Scout had already noticed something "only a lawyer's child could be expected to see..."
A jury never looks at a defendant it has convicted, and when this jury came in, not one of them looked at Tom Robinson.
Atticus had taken dead aim at both Bob and Mayella Ewell, tearing apart their stories about what had happened on the day that Tom Robinson had stopped by the Ewell house to help her. But in the end, the jury chose the Ewells' word over Tom's--just as Atticus had predicted.
Let's start with the rabid dog, Tim Johnson. What happens when the dog is first spotted? How do the people of Maycomb react to his presence in their town?
Got some ideas? Now think about other "diseases" (on a figurative level) that plague the town, and how the townspeople respond to the presence of such a cancerous attitude. Are their reactions similar?
You might also want to think about similarities between Tim Johnson (the dog) and other characters. Who else ends up dead? Are the townspeople afraid of any other characters? Do they ignore any other characters by figuratively closing their doors?
Now let's think about the verdict. I'm not sure if you're trying to make a connection between the rabid dog and the verdict, but the significance of the trial should be pretty obvious. Think about what the verdict means for the town, and whether or not it means something different for certain groups within the area.