Firstly, we don't know why the dog pulled away. We cannot tell that, the dog has not spoken.
Symbols and sigils, amulets and those kinds of things have energies attached to them; if you are wearing them, there is a chance that they are mixing with or changing your energies and so you are not exactly the same; your mind also knows you are wearing it and you may take on a sense of confidence or some other attitude because of what you believe the amulet does for you.
Much of magick lies in what we believe, if we believe we are safe and protected by an amulet, this will give us confidence. If we fear we are being attacked, then we give out the energy, posture and attitude of a fearful person.
I believe that the dog sensed something strong in you and felt afraid, he was protecting himself. I believe that you felt good in the amulet and this is why your energy changed.
There are 'secrets' in magickal symbols such as triangles, but you understand them as you grow magickally, they mean absolutely nothing unless you have come to understand them for yourself so its pointless speaking of them here.
To understand the triangle aspect (and the other aspects of your amulet) I suggest looking at it and meditating and writing down your thoughts, even making up a story might help here. You will understand it in a way that is 'secret', that is, it only really means something to you.
Hope this helps.
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