{
  "aliases": [
    "aa-similarity",
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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 $\\angle$ denote the [[angle at a point|0GJAJC6TNZ]].\nIf $\\angle BAC = \\angle B'A'C'$ and $\\angle CBA = \\angle C'B'A'$, then $ABC$ and $A'B'C'$ are [[similar|0YF6QXXWB5]].\n\n## Remarks\n\nBy the [[angle sum of a triangle|05MDKQBEAF]], the third angles are then equal too. So the criterion is also called angle-angle-angle similarity.\nAnother criterion for similarity is side-angle-side: two equal ratios of sides, and equal angles between those sides.\nIn hyperbolic geometry, triangles with equal angles are congruent, so the criterion has a different meaning there.\n\n## Explanations\n\n### L1 human\n\nThe shape of a triangle depends only on its angles. If two angles match, the third one matches too, since the three always add up to $\\pi$. So two triangles with matching angles are scaled copies of each other.\n",
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    "name": "Angle-angle similarity",
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        "locator": "Similar triangles",
        "url": "https://en.wikipedia.org/wiki/Similarity_(geometry)"
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  "markdown": "https://math2.tamnd.com/node/0NZVJYZVTZ.md",
  "msc": [
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  "name": "Angle-angle similarity",
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