AAA (Angle-Angle-Angle) Congruence Theorem?

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Drag the red points in the top half of the drawing to adjust the givens, then adjust the points to try to make congruent or non-congruent triangles in the bottom half.
Angle Angle Angle (AAA)
Is AAA enough to prove triangles congruent? If not, why not?
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Information: AAA (Angle-Angle-Angle) Congruence Theorem?