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Antiparallel Lines
In geometry, two line (geometry), lines l_1 and l_2 are antiparallel with respect to a given line m if they each make congruence (geometry), congruent angles with m in opposite Sense of rotation, senses. More generally, lines l_1 and l_2 are ''antiparallel'' with respect to another pair of lines m_1 and m_2 if they are antiparallel with respect to the angle bisector of m_1 and m_2. In any cyclic quadrilateral, any two opposite sides are antiparallel with respect to the other two sides. Relations # The line joining the feet to two altitude (triangle), altitudes of a triangle is antiparallel to the third side. (any cevians which 'see' the third side with the same angle create antiparallel lines) # The tangent to a triangle's circumcircle at a vertex is antiparallel to the opposite side. # The radius of the circumcircle at a vertex is perpendicular to all lines antiparallel to the opposite sides. Conic sections In an Cone#Elliptic cone, oblique cone, there are exactly two famil ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Geometry
Geometry (; ) is a branch of mathematics concerned with properties of space such as the distance, shape, size, and relative position of figures. Geometry is, along with arithmetic, one of the oldest branches of mathematics. A mathematician who works in the field of geometry is called a ''List of geometers, geometer''. Until the 19th century, geometry was almost exclusively devoted to Euclidean geometry, which includes the notions of point (geometry), point, line (geometry), line, plane (geometry), plane, distance, angle, surface (mathematics), surface, and curve, as fundamental concepts. Originally developed to model the physical world, geometry has applications in almost all sciences, and also in art, architecture, and other activities that are related to graphics. Geometry also has applications in areas of mathematics that are apparently unrelated. For example, methods of algebraic geometry are fundamental in Wiles's proof of Fermat's Last Theorem, Wiles's proof of Fermat's ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
