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I could have sworn you needed three pieces of information, including at least one side and one angle, to deduce all 6 pieces of information, of all sides and angles. But logically, it seems as though if you only know an angle and its opposite side length, even though you can't algebraically find it, visually there's nothing else that can vary, all other side lengths and angles have to be locked into place to keep that angle and its opposite side length the same.

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    $\begingroup$ Not quite. I think you're neglecting the tilt of the opposite side. Picture, for example, some angle with an opposite side. You can easily make a triangle—but now tilt that side one way or another. You can still make a triangle, but it'll have different angles and different side-lengths. $\endgroup$ Commented May 18, 2017 at 19:42
  • $\begingroup$ You need to know at least one side. You do not need to know any of the anlges. $SSS$ will prove congruence $AAA$ will not. $\endgroup$
    – Doug M
    Commented May 18, 2017 at 19:46
  • $\begingroup$ If you fix one side of a triangle $AB$ in place, the locus of points $C$ giving a certain angle at $C$ will be a union of two arcs of circles (or a circle if requiring a right angle at $C$). $\endgroup$ Commented May 18, 2017 at 19:49

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That is not true. Look at this picture: enter image description here

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  • $\begingroup$ Okay thank god or the universe or you or w/e, I was just only varying both sides or angles simultaneously, now I don't have to question everything I thought I knew about triangles. $\endgroup$
    – RayOfHope
    Commented May 18, 2017 at 19:46
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You need more information than this. For instance, if the perpendicular bisector of the side bisects the angle, that's one kind of triangle. But if it doesn't, that's another. A whole lot of others.

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