How do I affirm that a triangle defines a plane?

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I am trying to postulate the Euclidean plane surface. I have postulates of the straight line and of extending a straight line. I want to fill the gap between a triangle and a plane. How does a triangle define a plane? Is it postulated or axiomatic or other?

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This https://en.wikipedia.org/w/index.php?title=Hilbert's_axioms&oldid=942127286#I._Incidence link should "answer" your question. (I am intentionally using a history link: wikipedia may change and make me look like an idiot ... .)

But it does only sate properties of a plane. I would extend that to define a plane as the set of points on all the lines that intersect the triangle given by the points A,B,C (that are not all on the same line) in at least 2 pints.