Could you give me a little more information for the best answer I can give you?
What were the circumstances of the bite?
Was it a bite so serious it needed medical attention?
What sort of behavior work did you do?
What type of dog is this?
Has the dog bitten before?
my sister in law was petting him he jumped up bit her arm,, when she is around him he shows teeth, yes she went 2 hospital he broke the skin she got a jag, since he got knocked down he has a temper the work that got done was for his barkin and showing teeth it hasnt worked he is a border collie he has snaped at me 1 time
As he just broke the skin and didn't do a serious bite its your choice if you wish to try to work with him more with a behaviorist or if you wish to euthanize him as a danger to people and to yourself in terms of legal liability.
You can read about assessing a bite here
http://watchandtrain.com/dogtraining/blogs/thoughts/archive/2008/02/20/how-to-assess-the-severity-of-a-dog-bite.aspx
You mentioned he got knocked down. If this was a car accident I have seen myself that some dogs with head injuries may become unstable and unpredicatable in their reactions after such an accident.
My personal feeling on euthanasia is if you cannot protect others from your pet, and if the dog has shown that he will bite then your choices are limited to trying training or euthanasia. Its not fair to rehome a dog like this. If you don't tell the people he bites (or even if you do) you might still be found legally liable if he bites someone. On top of that the kind of people who want a dog that bites are usually not the sort of people you want to give your pet to.
I do not say to euthanize a pet lightly. But after years of doing rescue I know that unless training can change the dog's behavior so all including the dog are kept safe that euthanisia can be a better choice than many of the other options for the dog and the owner both. I know you'd hate to see headlines about your dog biting someone badly.
This might be a resolvable medical issue. Maybe your dog has a low thyroid, a too high a protein diet, a tick carried disease impacting behavior but if the dog is healthy and you can't change his responses to people then he is a danger to you and others.
Hope this helps you! Its a tough decision to make.
Dog Expert:Rescue, Train,Breed,Care
30+ yrs dog home vet care & nursing, rescue, behavior&training, responsible show breeding, genetics