{
  "aliases": [
    "pons-asinorum",
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  "body": "\n## Statement\n\nLet $ABC$ be a [[triangle|0CTNFGYMM2]] in a Euclidean space $\\mathbb{R}^n$ with $d(A, B) = d(A, C)$, where $d$ is the [[Euclidean distance|0NPPGHQNXQ]].\nThen the angles at $B$ and $C$ are equal: $\\angle ABC = \\angle ACB$.\n\n## Remarks\n\nThe converse holds too: if $\\angle ABC = \\angle ACB$ in a triangle $ABC$, then $d(A, B) = d(A, C)$.\nMathlib's form of the statement does not need that $A$, $B$ and $C$ are not collinear.\nIn an equilateral triangle, the theorem applies at each vertex. So all three angles are equal.\n\n## History\n\nThe statement is Proposition 5 of Book I of Euclid's Elements. Its Latin name is pons asinorum, \"the bridge of donkeys\".\n\n## Explanations\n\n### L1 human\n\nAn isosceles triangle has two equal sides, like the outline of a simple roof. The theorem says that the two base angles are then equal. Fold the triangle along the line from the top vertex to the midpoint of the base: the two halves match.\n",
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        "url": "https://en.wikipedia.org/wiki/Isosceles_triangle"
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  "name": "Isosceles triangle theorem",
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