{
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  "body": "\n## Statement\n\nLet $ABC$ and $A'B'C'$ be triangles in the Euclidean space $\\mathbb{R}^n$, and let $d$ be the [[Euclidean distance|0NPPGHQNXQ]].\nThen $ABC$ and $A'B'C'$ are [[congruent|093EDENVA1]] if and only if\n$$d(A, B) = d(A', B'), \\quad d(B, C) = d(B', C') \\quad \\text{and} \\quad d(C, A) = d(C', A').$$\n\n## Remarks\n\nOther criteria for congruence are side-angle-side, angle-side-angle and angle-angle-side.\nSide-side-angle is not a criterion: two sides and an angle that is not between them can fit two different triangles.\nAngle-angle-angle is not a criterion either. Triangles with equal angles are [[similar|0YF6QXXWB5]], but they can have different sizes.\n\n\n## Explanations\n\n### L1 human\n\nIf 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.\n",
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    "name": "Side-side-side congruence",
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  "msc": [
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  "name": "Side-side-side congruence",
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