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tuatara,
when socialized- that is, dogs who have learned about the rules of canine social interactions and use them appropriately - greet each other, they tend to:
approach on any variation of a curve - as opposed to what you may be accustomed to see in many situations where people greet each other/shake hands in a very direct, linear fashion, a 'straight line' from one greeter to another.
avoid eye contact.
in many human cultures, direct and sustained eye contact upon greeting and discussing is expected; eye contact between unknown adult dogs is considered 'strange' at best, and extremely provocative and threatening at most.
Head pats - tolerated by some dogs, but generally NOT preferred at all and many dogs would actively show you how "disliked" that gesture is.
Head patting, direct and sustained eye contact and linear, frontal interaction are all very "primate" ways of doing things- chimps and orangutans do the same things. They reach out with their hands, they hold hands, they pat each other. They hug. Dogs as a group dislike hugs. Some dogs have learned to tolerate or even enjoy a hug from a trusted human family member.
But it is not a natural activity for the majority of dogs.
The ideal way to approach a dog- and what I do - is, approach from a curvy angle; I literally bend a bit on approach. Not looking at dog. I approach from the side and may have a slightly open mouth , blinking <in dogs - closed mouth -can- equal tension; blinking can be a calming gesture>. I have my hand down and let the dog approach to smell. I try to approach from the side and with my back more toward the dog as opposed to my front body, and may even back up a bit to come in toward the dog's side. I crouch down alongside and let the dog investigate me from that angle. I always have one eye peeking over to see what the dog is telling me, without actually staring - so I can be ready to change what I'm doing, since canine body language is VERY fast and often VERY subtle. Once I got all those steps, then I move my hand toward the dog's chest and usually start any contact there. Always watching - a dog who had her mouth open and then she closes it - that's a change I need to be aware of.
That's a dog who I was told I could approach - or, in the case of the shelter dogs I work with - that I think I can approach. Upon seeing a dog, I usually make a quick decision based on the whole of the body language- should I even approach at all. Most times dogs are giving out small "distance-increasing" signals - don't come here, I'm worried- but people miss them because they are subtle.