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  "body": "\n## Definition\n\nLet $K$ be a field and let $\\mathcal{A}$ be an [[affine space|09XNAPTJQ7]] over a $K$-vector space.\nA triangle in $\\mathcal{A}$ is an ordered triple $(A, B, C)$ of points of $\\mathcal{A}$ that are not [[collinear|0AFNNTRTJE]]. It is written $ABC$ or $\\triangle ABC$.\nThe points $A$, $B$ and $C$ are its vertices. The segments $BC$, $CA$ and $AB$ are its sides.\n\n## Remarks\n\nThree points are not collinear if and only if they are affinely independent: the vectors $B - A$ and $C - A$ are linearly independent.\nIn a Euclidean space, the side lengths are often written $a = d(B, C)$, $b = d(C, A)$ and $c = d(A, B)$. The angles of the triangle are $\\angle BAC$, $\\angle CBA$ and $\\angle ACB$.\nA triangle is isosceles if two sides have the same length, equilateral if all three do, and scalene if no two do. It is a right triangle if one angle is $\\pi / 2$.\nMathlib's `Affine.Triangle` is an affinely independent family of three points, indexed by $\\{0, 1, 2\\}$.\n\n## Explanations\n\n### L1 human\n\nPick three points that are not on one straight line and join each pair. The result is a triangle. If the three points were on one line, the \"triangle\" would be flat, and it would have no area.\n",
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