Dogs are carnivores by nature, but that does not mean they cannot benefit from vegetables as well. The nutrients found in vegetables offer the same benefits to dogs as they do to humans. While some veggies--like broccoli, onions, chives and avocados--can prove toxic for dogs, veggies such as celery and carrots are perfectly safe.
Carrots provide fiber, beta carotene and antioxidants. Celery is an excellent source of calcium. Raw carrots and celery provide low-calorie sustenance for dogs and humans alike. In dogs, carrots and celery can also promote strong teeth, due to the chewing involved. If you find that your dog enjoys either of these foods, feel free to supplement them with the animal's regular food.
Raw or Cooked?
Raw vegetables like carrots and celery provide the greatest benefits to a dog's teeth, and also contain no loss in nutrients in enzymes. But if you have an older dog with sensitive teeth, or if you like to make your own dog food at home, you can mix in cooked carrots and celery without causing any harm.
Though vegetables like carrots and celery can provide beneficial nutrients, you should only give them to your dog in small amounts. They should not become a staple of your dog's diet, as dogs do not have the same carbohydrate requirements that humans do, and they require ample amounts of complete protein. But if you have some leftover carrots at the end of the night, or a few slices of celery lying around, you should have no concerns about sharing them with your dog.
What About Vegetarian Dogs?
There is still considerable debate as to whether dogs can safely adapt to a vegetarian or even vegan diet. Sites like PetMD strongly advise against it, arguing that dogs are evolutionarily hard-wired for meat consumption, while sites like Discovery's Planet Green disagree, arguing that dogs can adapt to a vegetarian or vegan lifestyle as long as they receive the proper nutrients. Regardless of which side is right, if your dog has a primarily commercial diet, you will still want to avoid over-supplementing with carrots and celery, in order to avoid inadvertently creating a nutrient imbalance.