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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 three ...
the distance between the two lines is the distance between the two intersection points of these lines with the perpendicular line. This distance can be found by first solving the linear systems. and. to get the coordinates of the intersection points. The solutions to the linear systems are the points.
Intercept theorem. On ratios of line segments formed when 2 intersecting lines are cut by a pair of parallels. The intercept theorem, also known as Thales's theorem, basic proportionality theorem or side splitter theorem, is an important theorem in elementary geometry about the ratios of various line segments that are created if two rays with a ...
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 the ...
In geometry, an intersection is a point, line, or curve common to two or more objects (such as lines, curves, planes, and surfaces). The simplest case in Euclidean geometry is the line–line intersection between two distinct lines, which either is one point (sometimes called a vertex) or does not exist (if the lines are parallel). Other types ...
Congruence (geometry) Relationship between two figures of the same shape and size, or mirroring each other. The two triangles on the left are congruent. The third is similar to them. The last triangle is neither congruent nor similar to any of the others. Congruence permits alteration of some properties, such as location and orientation, but ...
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A simplicial line arrangement (left) and a simple line arrangement (right). In geometry, an arrangement of lines is the subdivision of the Euclidean plane formed by a finite set of lines. An arrangement consists of bounded and unbounded convex polygons, the cells of the arrangment, line segments and rays, the edges of the arrangement, and ...
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