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Rope Riata
A rope used by a cowboy could be called a lasso, a lassoo, a lariat, a riata, or even just a rope!
It all depends for what purpose it is used...
lassos
* Added - lariats. Although the term lasso is often used, lasso is a verb describing use of a lariat.
Reata
A dogie is referring to cattle. So something that would be used to roundup cattle would be a Lasso, Lariat, Roper or Riata.