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Consequent of Playfair's axiom: a second line, parallel to the first, passing through the point. In geometry, Playfair's axiom is an axiom that can be used instead of the fifth postulate of Euclid (the parallel postulate ): In a plane, given a line and a point not on it, at most one line parallel to the given line can be drawn through the point ...
The distance (or perpendicular distance) from a point to a line is the shortest distance from a fixed point to any point on a fixed infinite line in Euclidean geometry. It is the length of the line segment which joins the point to the line and is perpendicular to the line. The formula for calculating it can be derived and expressed in several ways.
t. e. In geometry, a transversal is a line that passes through two lines in the same plane at two distinct points. Transversals play a role in establishing whether two or more other lines in the Euclidean plane are parallel. The intersections of a transversal with two lines create various types of pairs of angles: consecutive interior angles ...
t. e. In mathematics, affine geometry is what remains of Euclidean geometry when ignoring (mathematicians often say "forgetting" [1] [2]) the metric notions of distance and angle . As the notion of parallel lines is one of the main properties that is independent of any metric, affine geometry is often considered as the study of parallel lines.
Given the equations of two non-vertical parallel lines. 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. {\displaystyle {\begin {cases}y=mx+b_ {1}\\y=-x/m\,,\end {cases}}} and.
The angle bisector theorem states that the ratio of the length of the line segment BD to the length of segment CD is equal to the ratio of the length of side AB to the length of side AC : and conversely, if a point D on the side BC of ABC divides BC in the same ratio as the sides AB and AC, then AD is the angle bisector of angle ∠ A .
the distance between the two lines can be found by locating two points (one on each line) that lie on a common perpendicular to the parallel lines and calculating the distance between them. Since the lines have slope m , a common perpendicular would have slope −1/ m and we can take the line with equation y = − x / m as a common perpendicular.
In hyperbolic geometry, two lines are said to be ultraparallel if they do not intersect and are not limiting parallel . The ultraparallel theorem states that every pair of (distinct) ultraparallel lines has a unique common perpendicular (a hyperbolic line which is perpendicular to both lines).
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