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Perpendicular is also used as a noun: a perpendicular is a line which is perpendicular to a given line or plane. Perpendicularity is one particular instance of the more general mathematical concept of orthogonality ; perpendicularity is the orthogonality of classical geometric objects.
The line segments AB and CD are orthogonal to each other. In mathematics, orthogonality is the generalization of the geometric notion of perpendicularity.Whereas perpendicular is typically followed by to when relating two lines to one another (e.g., "line A is perpendicular to line B"), [1] orthogonal is commonly used without to (e.g., "orthogonal lines A and B").
Collinear – in the same line; Parallel – in the same direction. Transverse – intersecting at any angle, i.e. not parallel. Orthogonal (or perpendicular) – at a right angle (at the point of intersection). Elevation – along a curve from a point on the horizon to the zenith, directly overhead.
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. red angles are of equal size, ED and the tangent in B are antiparallel to AC and are perpendicular to MB
For example, adjacent angles of a parallelogram are supplementary, and opposite angles of a cyclic quadrilateral (one whose vertices all fall on a single circle) are supplementary. If a point P is exterior to a circle with center O, and if the tangent lines from P touch the circle at points T and Q, then ∠TPQ and ∠TOQ are supplementary.
In a three-dimensional Euclidean vector space, the orthogonal complement of a line through the origin is the plane through the origin perpendicular to it, and vice versa. [ 5 ] Note that the geometric concept of two planes being perpendicular does not correspond to the orthogonal complement, since in three dimensions a pair of vectors, one from ...
The straight lines which form right angles are called perpendicular. [8] Euclid uses right angles in definitions 11 and 12 to define acute angles (those smaller than a right angle) and obtuse angles (those greater than a right angle). [9] Two angles are called complementary if their sum is a right angle. [10]
The point P is the inversion point of Q; the polar is the line through P that is perpendicular to the line containing O, P and Q. If point R is the inverse of point P then the lines perpendicular to the line PR through one of the points is the polar of the other point (the pole). Poles and polars have several useful properties: