「図形の合同」の版間の差分
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=== 球面三角形の決定問題 ===
ユークリッド幾何のパターンに加え、[[球面幾何学|球面幾何]]や[[双曲幾何学|双曲幾何]]においては（三角形の内角の和が三角形の大きさを決定するから）'''AAA''' が（与えられた曲率の曲面上の）
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As with plane triangles, on a sphere two triangles sharing the same sequence of angle-side-angle (ASA) are necessarily congruent (that is, they have three identical sides and three identical angles).<ref name=Bolin>Michael Bolin, "Exploration of Spherical Geometry", September 9, 2003, pp.6-7. http://math.iit.edu/~mccomic/420/notes/Bolin_spherical.pdf</ref> This can be seen as follows: One can situate one of the vertices with a given angle at the south pole and run the side with given length up the prime meridian. Knowing both angles at either end of the segment of fixed length ensures that the other two sides emanate with a uniquely determined trajectory, and thus will meet each other at a uniquely determined point; thus ASA is valid.
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