Looking a dog in the eyes can be seen as a threat...
...funny thing is, I have that exact same effect on most Animals, small Children...
...and Folks in Authority...
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F....G-BPLF... 8-)...!
...how can one approach a Dog, without appearing to be a threat, and having one's hand bitten off when trying to pat/stroke it?......!
The safest way to approach any dog is backwards ..... it's the least threatening approach in the dogs head. If approaching forwards move with confidence and don't make eye contact or say anything don't attempt to touch the dog and don't smile at it as it's perceived as wanting to play ..... totally ignore it and talk to it's owner if it's on a lead if you are in someone's house the same rules apply . If the dog jumps up push it down firmly and turn your back on it and once again ignore it. If the dog starts to sniff you then it's saying hello ....slowly and with the back of your hand allow the dog to sniff you then start to stroke the dog under the chin, as this isn't as threatening as placing your hand over the dogs head. Once the dog has accepted you and if it's a well trained and handled dog, then it will allow you to stroke it all over.
The vast majority of problems with dogs are caused by the attitude and actions of the owners.
Dog's live in packs with one dog as the leader. As a dog owner you have to assume the pack leader roll and if you don't do that then the dog becomes the pack leader and will rule over anyone and everyone, that's why you have dogs that attack people and other dogs/animals, bark constantly, pull on the lead, jump up at people, escape constantly etc etc etc. The size and breed of the dog is irrelevant it is constantly looking for leadership, a Yorkie can dominate a Pit Bull terrier as long as it has the right attitude and projects the right energy. The same goes for humans approaching dogs ..... attitude and positive energy will calm most dogs.
If a dog is looking like it is going to attack then stand your ground and make yourself as big as possible, as most dogs are not going to attack and will read your confidence as dominance and will back off.
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