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Line art drawing of parallel lines and curves. In geometry, parallel lines are coplanar infinite straight lines that do not intersect at any point. Parallel planes are planes in the same three-dimensional space that never meet. Parallel curves are curves that do not touch each other or intersect and keep a fixed minimum distance.
In geometry, the parallel postulate, also called Euclid 's fifth postulate because it is the fifth postulate in Euclid's Elements, is a distinctive axiom in Euclidean geometry. It states that, in two-dimensional geometry: If a line segment intersects two straight lines forming two interior angles on the same side that are less than two right ...
For a convex quadrilateral with at most two parallel sides, the Newton line is the line that connects the midpoints of the two diagonals. [7] For a hexagon with vertices lying on a conic we have the Pascal line and, in the special case where the conic is a pair of lines, we have the Pappus line. Parallel lines are lines in the same plane that ...
If there are closest parallels to a given line they are known as the limiting parallel, asymptotic parallel or horoparallel (horo from Greek: ὅριον — border). For rays, the relation of limiting parallel is an equivalence relation, which includes the equivalence relation of being coterminal. If, in a hyperbolic triangle, the pairs of ...
convex. In Euclidean geometry, a parallelogram is a simple (non- self-intersecting) quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure. The congruence of opposite sides and opposite angles is a direct consequence of ...
As affine geometry deals with parallel lines, one of the properties of parallels noted by Pappus of Alexandria has been taken as a premise: [9] [10] Suppose A, B, C are on one line and A', B', C' on another. If the lines AB' and A'B are parallel and the lines BC' and B'C are parallel, then the lines CA' and C'A are parallel.
A vanishing point is a point on the image plane of a perspective rendering where the two-dimensional perspective projections of mutually parallel lines in three-dimensional space appear to converge. When the set of parallel lines is perpendicular to a picture plane, the construction is known as one-point perspective, and their vanishing point ...
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