cuts of meat for dogs to eat

I called in at the local butcher's yesterday, looking for some meat for Penny. When I asked him exactly what a brisket bone is, he folded his arms, leaned back against the wall and said, "Well, where's your brisket?"
I stared at him. No idea. It did occur to me that the word sounds like 'breast' - but no way was I going there...
"People these days just don't know their cuts of meat," he said."Come on, think about it. Where would your brisket be?"
The other butcher grinned at me from behind him, but I thought she seemed sympathetic, so perhaps I'm not the only one to get the 'treatment' from her boss.
It was all beginning to seem a bit hard. I only asked about the brisket because I'd been told it's a soft bone. I'm obviously still stressing about the fact that Penny broke a tooth on a bone (we think) and had to have it extracted. (The tooth, not the bone.)
Of course he had a chart on the wall, didn't he? Determined to educate the uninformed member of the public, he showed me the brisket bone, laughing at my naive suggestion that it might perhaps be a rib. I don't feel quite so dumb not knowing, because he told me a brisket isn't a bone at all. It's cartilage and connects the two sides of the chest. That would account for wiser dog-owners having told me it's safe to eat.

But when I looked on the Net, the mystery deepened, because The American Heritage Dictionary defines it as "The chest of an animal. 2. The ribs and meat taken from the chest of an animal." That might explain why, the last time I asked for a brisket bone, I got a whole heap of rib bones. The Concise Oxford Dictionary says it's the "breast of a beast".
At MeatTrade.com there's a list with photos of a range of cuts of meat and there's a boneless brisket, so I guess that's where the brisket bones for dogs come from.