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• 類似中線（るいじちゅうせん）は任意の三角形に対して定義される3本の線である。類似中線は、三角形の角の二等分線を対称軸として、中線と対称の位置にある直線である。3本の直線は1点で交わる。この点は類似重心またはルモワーヌ点と呼ばれる。
• Symmedians are three particular geometrical lines associated with every triangle. They are constructed by taking a median of the triangle (a line connecting a vertex with the midpoint of the opposite side), and reflecting the line over the corresponding angle bisector (the line through the same vertex that divides the angle there in half). The angle formed by the symmedian and the angle bisector has the same measure as the angle between the median and the angle bisector, but it is on the other side of the angle bisector.Many times in geometry, if we take three special lines through the vertices of a triangle, or cevians, then their reflections about the angle bisector, called isogonal lines, will also have interesting properties. For instance, if three cevians of a triangle intersect at a point P, then their isogonal lines also intersect at a point, called the isogonal conjugate of P.The symmedians illustrate this fact nicely. In the diagram, the medians (in blue) intersect at the centroid G. Because the symmedians (in red) are isogonal to the medians, the symmedians also intersect at a single point, K. This point is called the triangle's symmedian point, or alternatively the Lemoine point or Grebe point.The green lines are the angle bisectors; note how the symmedians and medians are symmetric about the angles bisectors (hence the name "symmedian.")
• So wie man eine Seitenhalbierende eines Dreiecks auch als Mediane bezeichnet, nennt man das Spiegelbild einer Seitenhalbierenden an der entsprechenden Winkelhalbierenden (also an der Winkelhalbierenden, die von derselben Ecke ausgeht wie die Seitenhalbierende) Symmediane. Der Begriff ist eine Abkürzung für "symmetrische Mediane", kommt aus dem Griechischen und bedeutet "Spiegelung an der Mittellinie".Die drei Symmedianen eines Dreiecks schneiden einander in einem Punkt, dem so genannten lemoineschen Punkt (Lemoinepunkt), der auch Grebepunkt oder Symmedianenpunkt genannt wird. Dies lässt sich mit Hilfe des Satzes von Ceva beweisen.Der Schnittpunkt der Symmedianen ist ein nicht-kanonischer ausgezeichneter Punkt des Dreiecks.
• Symediana to prosta Cevy będąca odbiciem symetrycznym środkowej trójkąta względem dwusiecznej wychodzącej z tego samego wierzchołka. Symediany przecinają się w jednym punkcie (zwanym punktem Lemoine'a), jak wiele innych charakterystycznych prostych Cevy.
• 대칭중선(Symmedian)이란, 삼각형에서 중선을 각대칭시킨 선이다.즉, 삼각형 ABC에서 A에 대한 대칭중선은 A에 대한 중선과 등편각선이다.또한 삼각형의 세 대칭중선의 교점을 대칭중심(Symmedian point)이라 한다.즉 대칭중심은 무게중심의 등각켤레점이다.
• Симедиана — чевиана треугольника, луч которой симметричен лучу медианы относительно биссектрисы угла, проведенной из той же вершины.
• In geometra, la simmediana è un segmento simmetrico alla mediana rispetto alla bisettrice dello stesso vertice.Dato un triangolo ABC conduciamo le bisettrici interne AL, BM, CN e le mediane AA', BB, CC, quindi determiniamo la simmetrica della mediana rispetto alla bisettrice; indichiamo con R, S, T i punti d'intersezione delle simmetriche rispettivamente con i lati BC, AC, AB, abbiamo così tre nuovi segmenti AR, BS, CT, che vengono chiamati simediane del triangolo.
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• 類似中線（るいじちゅうせん）は任意の三角形に対して定義される3本の線である。類似中線は、三角形の角の二等分線を対称軸として、中線と対称の位置にある直線である。3本の直線は1点で交わる。この点は類似重心またはルモワーヌ点と呼ばれる。
• Symediana to prosta Cevy będąca odbiciem symetrycznym środkowej trójkąta względem dwusiecznej wychodzącej z tego samego wierzchołka. Symediany przecinają się w jednym punkcie (zwanym punktem Lemoine'a), jak wiele innych charakterystycznych prostych Cevy.
• 대칭중선(Symmedian)이란, 삼각형에서 중선을 각대칭시킨 선이다.즉, 삼각형 ABC에서 A에 대한 대칭중선은 A에 대한 중선과 등편각선이다.또한 삼각형의 세 대칭중선의 교점을 대칭중심(Symmedian point)이라 한다.즉 대칭중심은 무게중심의 등각켤레점이다.
• Симедиана — чевиана треугольника, луч которой симметричен лучу медианы относительно биссектрисы угла, проведенной из той же вершины.
• In geometra, la simmediana è un segmento simmetrico alla mediana rispetto alla bisettrice dello stesso vertice.Dato un triangolo ABC conduciamo le bisettrici interne AL, BM, CN e le mediane AA', BB, CC, quindi determiniamo la simmetrica della mediana rispetto alla bisettrice; indichiamo con R, S, T i punti d'intersezione delle simmetriche rispettivamente con i lati BC, AC, AB, abbiamo così tre nuovi segmenti AR, BS, CT, che vengono chiamati simediane del triangolo.
• Symmedians are three particular geometrical lines associated with every triangle. They are constructed by taking a median of the triangle (a line connecting a vertex with the midpoint of the opposite side), and reflecting the line over the corresponding angle bisector (the line through the same vertex that divides the angle there in half).
• So wie man eine Seitenhalbierende eines Dreiecks auch als Mediane bezeichnet, nennt man das Spiegelbild einer Seitenhalbierenden an der entsprechenden Winkelhalbierenden (also an der Winkelhalbierenden, die von derselben Ecke ausgeht wie die Seitenhalbierende) Symmediane.
rdfs:label
• Symédiane
• Simmediana
• Symediana
• Symmedian
• Symmediane
• Симедиана
• 類似中線
• 대칭중선
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