At first you might think that to articulate a thesis (or thesis statement) simply means to state it. When you write a paper you'll need to put a thesis statement into words. Your thesis statement could be a simple sentence such as this:
 Example of a simple thesis statement: "Dogs are the best pets."
If a thesis (or thesis statement) could stand alone, without reasons or supporting arguments or evidence, there wouldn't be any reason to "articulate" the thesis beyond merely stating it. You could write the thesis sentence -- Dogs are the best pets, for example -- and you'd be done. We know this isn't how things work.
On reflection it seems obvious that the very idea of a thesis statement says that it needs elaboration and support. In this guide, we call the work of developing reasons, finding and looking at evidence, presenting evidence and arguments, and so forth -- making your thesis convincing to your reader -- "articulating the thesis."
A better (and better articulated) thesis statement might be one like this:
 "Dogs are the best pets because they are loyal, watch for intruders, and actually make their owners healthier."
However, even though example  includes reasons, it still lacks full development. It would be hard for a reader -- almost any reader -- to take the thesis as complete. If we think critically about it, we want more evidence, more complete arguments, plus consideration of counter arguments and other points of view. What's needed is the full development with evidence, reasons, qualifications, limits, etc., that might convince an actual reader.
In other words, a thesis (and especially a thesis that will be adequate for a college writing assignment) needs the full articulation of a whole paper.
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