Girth
The girth is the strap that runs under the belly and holds the saddle in place.

What is it for?
It fastens the saddle to the horse so it does not slip.
More about this item
The girth runs from one billet strap under the belly to the other. It comes in leather, neoprene or braided material, sometimes shaped behind the elbow.
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Sources: British Horse Society · The Pony Club (UK). Descriptive only; not care or training advice.