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In geometry, a parallelogon is a polygon with parallel opposite sides (hence the name) that can tile a plane by translation (rotation is not permitted). [ 1 ] [ 2 ] Parallelogons have an even number of sides and opposite sides that are equal in length.
The centers of four squares all constructed either internally or externally on the sides of a parallelogram are the vertices of a square. [8] If two lines parallel to sides of a parallelogram are constructed concurrent to a diagonal, then the parallelograms formed on opposite sides of that diagonal are equal in area. [8]
The ratio of the areas of each pair of adjacent triangles is the same as that between the lengths of the parallel sides. [15] Let the trapezoid have vertices A, B, C, and D in sequence and have parallel sides AB and DC. Let E be the intersection of the diagonals, and let F be on side DA and G be on side BC such that FEG is parallel to AB and CD.
Individual polygons are named (and sometimes classified) according to the number of sides, combining a Greek-derived numerical prefix with the suffix -gon, e.g. pentagon, dodecagon. The triangle, quadrilateral and nonagon are exceptions, although the regular forms trigon, tetragon, and enneagon are sometimes encountered as well.
In geometry, a polygon (/ ˈ p ɒ l ɪ ɡ ɒ n /) is a plane figure made up of line segments connected to form a closed polygonal chain. The segments of a closed polygonal chain are called its edges or sides. The points where two edges meet are the polygon's vertices or corners. An n-gon is a polygon with n sides; for example, a triangle is a 3 ...
Coxeter states that every zonogon (a 2m-gon whose opposite sides are parallel and of equal length) can be dissected into 1 ⁄ 2 m(m − 1) parallelograms. [5] In particular this is true for regular polygons with evenly many sides, in which case the parallelograms are all rhombi.
Any of the sides of a parallelogram, or either (but typically the longer) of the parallel sides of a trapezoid can be considered its base. Sometimes the parallel opposite side is also called a base, or sometimes it is called a top, apex, or summit. The other two edges can be called the sides.
A rectilinear polygon is a polygon all of whose sides meet at right angles. Thus the interior angle at each vertex is either 90° or 270°. Rectilinear polygons are a special case of isothetic polygons. In many cases another definition is preferable: a rectilinear polygon is a polygon with sides parallel to the axes of Cartesian coordinates ...