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This is a list of two-dimensional geometric shapes in Euclidean and other geometries. For mathematical objects in more dimensions, see list of mathematical shapes . For a broader scope, see list of shapes .
A parallelogram is (under the inclusive definition) a trapezoid with two pairs of parallel sides. A parallelogram has central 2-fold rotational symmetry (or point reflection symmetry). It is possible for obtuse trapezoids or right trapezoids (rectangles). A tangential trapezoid is a trapezoid that has an incircle.
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.
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 ...
A regular digon has both angles equal and both sides equal and is represented by Schläfli symbol {2}. It may be constructed on a sphere as a pair of 180 degree arcs connecting antipodal points, when it forms a lune. The digon is the simplest abstract polytope of rank 2. A truncated digon, t{2} is a square, {4}. An alternated digon, h{2} is a ...
Ridge, an (n-2)-dimensional element Peak , an ( n -3)-dimensional element For example, in a polyhedron (3-dimensional polytope), a face is a facet, an edge is a ridge, and a vertex is a peak.
Isosceles trapezium (UK) or isosceles trapezoid (US): one pair of opposite sides are parallel and the base angles are equal in measure. Alternative definitions are a quadrilateral with an axis of symmetry bisecting one pair of opposite sides, or a trapezoid with diagonals of equal length. Parallelogram: a quadrilateral with two pairs of ...
A rhombus therefore has all of the properties of a parallelogram: for example, opposite sides are parallel; adjacent angles are supplementary; the two diagonals bisect one another; any line through the midpoint bisects the area; and the sum of the squares of the sides equals the sum of the squares of the diagonals (the parallelogram law).
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