Side-side-side congruence

Statement

Let $ABC$ and $A'B'C'$ be triangles in the Euclidean space $\mathbb{R}^n$, and let $d$ be the Euclidean distance. Then $ABC$ and $A'B'C'$ are congruent if and only if $$d(A, B) = d(A', B'), \quad d(B, C) = d(B', C') \quad \text{and} \quad d(C, A) = d(C', A').$$

Remarks

Other criteria for congruence are side-angle-side, angle-side-angle and angle-angle-side. Side-side-angle is not a criterion: two sides and an angle that is not between them can fit two different triangles. Angle-angle-angle is not a criterion either. Triangles with equal angles are similar, but they can have different sizes.

Explanations

L1 human

If you know the three side lengths of a triangle, you know the whole triangle. Three sticks of fixed lengths make one rigid shape, up to a turn or a flip. This is why triangles make frames stiff.