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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.
Each of a triangle's excircles (orange) is tangent to one of the triangle's sides and to the other two extended sides. In plane geometry, an extended side or sideline of a polygon is the line that contains one side of the polygon. The extension of a finite side (a line segment) into an infinite line arises in various contexts.
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]
The base regularity of a pyramid's base may be classified based on the type of polygon: one example is the star pyramid in which its base is the regular star polygon. [24] The truncated pyramid is a pyramid cut off by a plane; if the truncation plane is parallel to the base of a pyramid, it is called a frustum.
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 DEF is called the pedal triangle of P. [17] The antipedal triangle of P is the triangle formed by the lines through A, B, C perpendicular to PA, PB, PC respectively. Two points P and Q are called counter points if the pedal triangle of P is homothetic to the antipedal triangle of Q and the pedal triangle of Q is homothetic to the ...
In an isosceles triangle that has exactly two equal sides, the equal sides are called legs and the third side is called the base. The angle included by the legs is called the vertex angle and the angles that have the base as one of their sides are called the base angles. [6] The vertex opposite the base is called the apex. [7]