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In geometry, a trapezoid (/ ˈtræpəzɔɪd /) in North American English, or trapezium (/ trəˈpiːziəm /) in British English, [ 1 ][ 2 ] is a quadrilateral that has one pair of parallel sides. The parallel sides are called the bases of the trapezoid. The other two sides are called the legs (or the lateral sides) if they are not parallel ...
A square is a special case of a rhombus (equal sides, opposite equal angles), a kite (two pairs of adjacent equal sides), a trapezoid (one pair of opposite sides parallel), a parallelogram (all opposite sides parallel), a quadrilateral or tetragon (four-sided polygon), and a rectangle (opposite sides equal, right-angles), and therefore has all ...
A quadrilateral is a square if and only if it is both a rhombus and a rectangle (i.e., four equal sides and four equal angles). Oblong: longer than wide, or wider than long (i.e., a rectangle that is not a square). [ 5 ] Kite: two pairs of adjacent sides are of equal length.
Since and are both perpendicular to , they are parallel and so the quadrilateral is a trapezoid. The theorem is proved by computing the area of this trapezoid in two different ways. The theorem is proved by computing the area of this trapezoid in two different ways.
Quadrilateral – 4 sides Cyclic quadrilateral; Kite; Parallelogram. Rhombus (equilateral parallelogram) Lozenge; Rhomboid; Rectangle; Square (regular quadrilateral) Tangential quadrilateral; Trapezoid. Isosceles trapezoid; Pentagon – 5 sides; Hexagon – 6 sides Lemoine hexagon; Heptagon – 7 sides; Octagon – 8 sides; Nonagon – 9 sides ...
Ptolemy's theorem is a relation among these lengths in a cyclic quadrilateral. In Euclidean geometry, Ptolemy's theorem is a relation between the four sides and two diagonals of a cyclic quadrilateral (a quadrilateral whose vertices lie on a common circle). The theorem is named after the Greek astronomer and mathematician Ptolemy (Claudius ...
Any non-self-crossing quadrilateral that has an axis of symmetry must be either a kite, with a diagonal axis of symmetry; or an isosceles trapezoid, with an axis of symmetry through the midpoints of two sides. These include as special cases the rhombus and the rectangle respectively, and the square, which is a special case of both. [1]
An orthodiagonal quadrilateral (yellow). According to the characterization of these quadrilaterals, the two red squares on two opposite sides of the quadrilateral have the same total area as the two blue squares on the other pair of opposite sides. In Euclidean geometry, an orthodiagonal quadrilateral is a quadrilateral in which the diagonals ...