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A crossed rectangle is a crossed (self-intersecting) quadrilateral which consists of two opposite sides of a rectangle along with the two diagonals [4] (therefore only two sides are parallel). It is a special case of an antiparallelogram , and its angles are not right angles and not all equal, though opposite angles are equal.
The lengths of the horizontal sides of the original square and the four root rectangles derived from it, are respectively ,,,,. [ 2 ] A root rectangle is a rectangle in which the ratio of the longer side to the shorter is the square root of an integer , such as √ 2 , √ 3 , etc. [ 2 ]
If an horizontal line is drawn through the intersection point of the diagonal and the internal edge of the square, the original golden rectangle and the two scaled copies along the diagonal have linear sizes in the ratios ::, the square and rectangle opposite the diagonal both have areas equal to . [10]
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 ...
In any isosceles trapezoid, two opposite sides (the bases) are parallel, and the two other sides (the legs) are of equal length (properties shared with the parallelogram), and the diagonals have equal length. The base angles of an isosceles trapezoid are equal in measure (there are in fact two pairs of equal base angles, where one base angle is ...
As n approaches infinity, the internal angle approaches 180 degrees. For a regular polygon with 10,000 sides (a myriagon) the internal angle is 179.964°. As the number of sides increases, the internal angle can come very close to 180°, and the shape of the polygon approaches that of a circle. However the polygon can never become a circle.
A rectangle, <4>, is a convex direct equiangular polygon, containing four 90° internal angles. A concave indirect equiangular polygon, <6-2>, like this hexagon, counterclockwise, has five left turns and one right turn, like this tetromino. A skew polygon has equal angles off a plane, like this skew octagon alternating red and blue edges on a cube.
A rhombus has opposite angles equal, while a rectangle has opposite sides equal. A rhombus has an inscribed circle, while a rectangle has a circumcircle. A rhombus has an axis of symmetry through each pair of opposite vertex angles, while a rectangle has an axis of symmetry through each pair of opposite sides. The diagonals of a rhombus ...