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In geometry, the hinge theorem (sometimes called the open mouth theorem) states that if two sides of one triangle are congruent to two sides of another triangle, and the included angle of the first is larger than the included angle of the second, then the third side of the first triangle is longer than the third side of the second triangle. This theorem is given as Proposition 24 in Book I of Euclid's Elements.

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  • Hinge theorem (en)
  • Scharnierstelling (nl)
  • 樞紐定理 (zh)
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  • In geometry, the hinge theorem (sometimes called the open mouth theorem) states that if two sides of one triangle are congruent to two sides of another triangle, and the included angle of the first is larger than the included angle of the second, then the third side of the first triangle is longer than the third side of the second triangle. This theorem is given as Proposition 24 in Book I of Euclid's Elements. (en)
  • De scharnierstelling is een stelling uit de meetkunde die zegt dat als van twee driehoeken die twee gelijke zijden hebben, de hoek tussen deze zijden bij de ene driehoek groter is dan bij de andere, ook de derde zijde van die driehoek groter is dan bij de andere. Deze stelling is eigenlijk Propositie 24 van Boek 1 van de Elementen van Euclides, en wordt wel de openmondstelling genoemd. In symbolen: Laat ABC en A'B'C' de twee diehoeken zijn met gelijke zijden AB = A'B' en AC = A'C', en zij ∠BAC > ∠ B'A'C'; dan is ook BC > B'C'. (nl)
  • 樞紐定理是一個平面几何定理，是三角形的基本性質之一，通常會以兩組三角形作比較。若有兩組三角形，這兩個三角形有兩組對應邊相等，則三角形的邊所夾的角，角度愈大，則三角形的第三邊也愈大。樞紐定理也有和逆定理之分，正性質是由夾角的角度大小推出第三邊的長短，而逆性質則是由第三邊的長短來推出對角夾角角度大小。 (zh)
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  • In geometry, the hinge theorem (sometimes called the open mouth theorem) states that if two sides of one triangle are congruent to two sides of another triangle, and the included angle of the first is larger than the included angle of the second, then the third side of the first triangle is longer than the third side of the second triangle. This theorem is given as Proposition 24 in Book I of Euclid's Elements. (en)
  • De scharnierstelling is een stelling uit de meetkunde die zegt dat als van twee driehoeken die twee gelijke zijden hebben, de hoek tussen deze zijden bij de ene driehoek groter is dan bij de andere, ook de derde zijde van die driehoek groter is dan bij de andere. Deze stelling is eigenlijk Propositie 24 van Boek 1 van de Elementen van Euclides, en wordt wel de openmondstelling genoemd. In symbolen: Laat ABC en A'B'C' de twee diehoeken zijn met gelijke zijden AB = A'B' en AC = A'C', en zij ∠BAC > ∠ B'A'C'; dan is ook BC > B'C'. (nl)
  • 樞紐定理是一個平面几何定理，是三角形的基本性質之一，通常會以兩組三角形作比較。若有兩組三角形，這兩個三角形有兩組對應邊相等，則三角形的邊所夾的角，角度愈大，則三角形的第三邊也愈大。樞紐定理也有和逆定理之分，正性質是由夾角的角度大小推出第三邊的長短，而逆性質則是由第三邊的長短來推出對角夾角角度大小。 (zh)
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