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A triangle is a polygon with three corners and three sides, one of the basic shapes in geometry.The corners, also called vertices, are zero-dimensional points while the sides connecting them, also called edges, are one-dimensional line segments.
These segments are called its edges or sides, and the points where two of the edges meet are the polygon's vertices (singular: vertex) or corners. The word polygon comes from Late Latin polygōnum (a noun), from Greek πολύγωνον ( polygōnon/polugōnon ), noun use of neuter of πολύγωνος ( polygōnos/polugōnos , the masculine ...
In geometry, a triangle center or triangle centre is a point in the triangle's plane that is in some sense in the middle of the triangle. For example, the centroid , circumcenter , incenter and orthocenter were familiar to the ancient Greeks , and can be obtained by simple constructions .
In geometry, a polygon (/ ˈ p ɒ l ɪ ɡ ɒ n /) is a plane figure made up of line segments connected to form a closed polygonal chain. The segments of a closed polygonal chain are called its edges or sides. The points where two edges meet are the polygon's vertices or corners. An n-gon is a polygon with n sides; for example, a triangle is a 3 ...
Fig 1. Construction of the first isogonic center, X(13). When no angle of the triangle exceeds 120°, this point is the Fermat point. In Euclidean geometry, the Fermat point of a triangle, also called the Torricelli point or Fermat–Torricelli point, is a point such that the sum of the three distances from each of the three vertices of the triangle to the point is the smallest possible [1] or ...
In a triangle, any arbitrary side can be considered the base. The two endpoints of the base are called base vertices and the corresponding angles are called base angles. The third vertex opposite the base is called the apex. The extended base of a triangle (a particular case of an extended side) is the line that contains the base.
The center of the first Lemoine circle lies midway between the circumcenter and the lemoine point of the triangle, The points of intersections of the antiparallels to the sides of triangle ABC through the Lemoine point of a triangle ABC lie on a circle called the second Lemoine circle or the cosine circle of triangle ABC. The name "cosine ...
The area of a triangle then falls out as the case of a polygon with three sides. While the line integral method has in common with other coordinate-based methods the arbitrary choice of a coordinate system, unlike the others it makes no arbitrary choice of vertex of the triangle as origin or of side as base.