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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.
An altitude of a triangle is a straight line through a vertex and perpendicular to the opposite side. This opposite side is called the base of the altitude, and the point where the altitude intersects the base (or its extension) is called the foot of the altitude. [23] The length of the altitude is the distance between the base and the vertex.
In geometry, a Cartesian coordinate system (UK: / k ɑːr ˈ t iː zj ə n /, US: / k ɑːr ˈ t iː ʒ ə n /) in a plane is a coordinate system that specifies each point uniquely by a pair of real numbers called coordinates, which are the signed distances to the point from two fixed perpendicular oriented lines, called coordinate lines ...
Taking L to be the x-axis, the line integral between consecutive vertices (x i,y i) and (x i+1,y i+1) is given by the base times the mean height, namely (x i+1 − x i)(y i + y i+1)/2. The sign of the area is an overall indicator of the direction of traversal, with negative area indicating counterclockwise traversal.
Let ABC be a plane triangle and let ( x : y : z) be the trilinear coordinates of an arbitrary point in the plane of triangle ABC. A straight line in the plane of triangle ABC whose equation in trilinear coordinates has the form f ( a, b, c) x + g ( a, b, c) y + h ( a, b, c) z = 0. where the point with trilinear coordinates ( f ( a, b, c) : g ...
Let ABC be a plane triangle and let x : y : z be the trilinear coordinates of an arbitrary point in the plane of triangle ABC.. A straight line in the plane of ABC whose equation in trilinear coordinates has the form (,,) + (,,) + (,,) = where the point with trilinear coordinates (,,): (,,): (,,) is a triangle center, is a central line in the plane of ABC relative to ABC.
The triangle has 3 vertices, each of which pairs with another triangle's vertex, making up another 3 edges. These edges form 3 parallelograms as other faces. [2] If the prism's edges are perpendicular to the base, the lateral faces are rectangles, and the prism is called a right triangular prism. [3]
Let the centroids of these triangles be X, Y, Z respectively. Then the lines AX, BY, CZ are concurrent. The point of concurrence N 1 is the first Napoleon point, or the outer Napoleon point, of the triangle ABC. The triangle XYZ is called the outer Napoleon triangle of ABC. Napoleon's theorem asserts that this triangle is an equilateral triangle.