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Median Triangle
The median triangle of a given (reference) triangle is a triangle A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices ''A'', ''B'', and ''C'' is denoted \triangle ABC. In Euclidean geometry, any three points, when non- colline ..., the sides of which are equal and parallel to the medians of its reference triangle. The area of the median triangle is \tfrac of the area of its reference triangle, and the median triangle of the median triangle is similar to the reference triangle of the first median triangle with a scaling factor of \tfrac. References *Roger A. Johnson: ''Advanced Euclidean Geometry''. Dover 2007, , pp. 282–283 *Claudi Alsina, Roger B. Nelsen: ''Charming Proofs: A Journey Into Elegant Mathematics''. MAA, 2010, , p. 165 *Árpad Bényi, Branko Ćurgus: "Outer Median Triangles". In: ''Mathematics Magazine'', Vol. 87, No. 3 (June 2014), pp. 185–194JSTOR External links * {{DEF ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Median Triangle
The median triangle of a given (reference) triangle is a triangle A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices ''A'', ''B'', and ''C'' is denoted \triangle ABC. In Euclidean geometry, any three points, when non- colline ..., the sides of which are equal and parallel to the medians of its reference triangle. The area of the median triangle is \tfrac of the area of its reference triangle, and the median triangle of the median triangle is similar to the reference triangle of the first median triangle with a scaling factor of \tfrac. References *Roger A. Johnson: ''Advanced Euclidean Geometry''. Dover 2007, , pp. 282–283 *Claudi Alsina, Roger B. Nelsen: ''Charming Proofs: A Journey Into Elegant Mathematics''. MAA, 2010, , p. 165 *Árpad Bényi, Branko Ćurgus: "Outer Median Triangles". In: ''Mathematics Magazine'', Vol. 87, No. 3 (June 2014), pp. 185–194JSTOR External links * {{DEF ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Triangle
A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices ''A'', ''B'', and ''C'' is denoted \triangle ABC. In Euclidean geometry, any three points, when non- collinear, determine a unique triangle and simultaneously, a unique plane (i.e. a two-dimensional Euclidean space). In other words, there is only one plane that contains that triangle, and every triangle is contained in some plane. If the entire geometry is only the Euclidean plane, there is only one plane and all triangles are contained in it; however, in higher-dimensional Euclidean spaces, this is no longer true. This article is about triangles in Euclidean geometry, and in particular, the Euclidean plane, except where otherwise noted. Types of triangle The terminology for categorizing triangles is more than two thousand years old, having been defined on the very first page of Euclid's Elements. The names used for modern classification are ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Median (geometry)
In geometry, a median of a triangle is a line segment joining a vertex to the midpoint of the opposite side, thus bisecting that side. Every triangle has exactly three medians, one from each vertex, and they all intersect each other at the triangle's centroid. In the case of isosceles and equilateral triangles, a median bisects any angle at a vertex whose two adjacent sides are equal in length. The concept of a median extends to tetrahedra. Relation to center of mass Each median of a triangle passes through the triangle's centroid, which is the center of mass of an infinitely thin object of uniform density coinciding with the triangle. Thus the object would balance on the intersection point of the medians. The centroid is twice as close along any median to the side that the median intersects as it is to the vertex it emanates from. Equal-area division Each median divides the area of the triangle in half; hence the name, and hence a triangular object of uniform density would ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
