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Because parallel lines in a Euclidean plane are equidistant there is a unique distance between the two parallel lines. Given the equations of two non-vertical, non-horizontal parallel lines, = + = +, 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 ...
A simple (non-self-intersecting) quadrilateral is a parallelogram if and only if any one of the following statements is true: [2] [3] Two pairs of opposite sides are parallel (by definition). Two pairs of opposite sides are equal in length. Two pairs of opposite angles are equal in measure. The diagonals bisect each other.
The distance between two parallel lines in the plane is the minimum distance between any two points. Formula and proof. Because the lines are parallel, the ...
The other two sides are called the legs (or the lateral sides) if they are not parallel; otherwise, the trapezoid is a parallelogram, and there are two pairs of bases. A scalene trapezoid is a trapezoid with no sides of equal measure, [ 3 ] in contrast with the special cases below.
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 ...
Two lines are parallel if and only if the two angles of any pair of consecutive interior angles of any transversal are supplementary (sum to 180°). Proposition 1.28 of Euclid's Elements , a theorem of absolute geometry (hence valid in both hyperbolic and Euclidean Geometry ), proves that if the angles of a pair of consecutive interior angles ...
A parallelogon is constructed by two or three pairs of parallel line segments. The vertices and edges on the interior of the hexagon are suppressed. There are five Bravais lattices in two dimensions, related to the parallelogon tessellations by their five symmetry variations.
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. (This is the affine version of Pappus's hexagon theorem). The full axiom system proposed has point, line, and line containing point as primitive notions: Two points are contained in just one line.