Types of quadrilaterals

In geometry, a square is a regular quadrilateral. It has four straight sides of equal length and four equal angles. Squares are special cases of rectangles, which have four equal angles, and of rhombuses, which have four equal sides. As with all rectangles, a square's angles are right angles (90 degrees, or Pi|/2 radians), making adjacent sides perpendicular. The area of a square is the side length multiplied by itself, and so in algebra, multiplying a number by itself is called squaring.

In Euclidean plane geometry, a rectangle is a rectilinear convex polygon or a quadrilateral with four right angles. It can also be defined as: an equiangular quadrilateral, since equiangular means that all of its angles are equal (360°/4 = 90°); or a parallelogram containing a right angle. A rectangle with four sides of equal length is a square. The term "oblong" is used to refer to a non-square rectangle. A rectangle with vertices ABCD would be denoted as .

280px|thumb|The rhombus has a square as a special case, and is a special case of a Kite (geometry)|kite and [[parallelogram.]]

In Euclidean geometry, a parallelogram is a simple (non-self-intersecting) quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure. The congruence of opposite sides and opposite angles is a direct consequence of the Euclidean parallel postulate and neither condition can be proven without appealing to the Euclidean parallel postulate or one of its equivalent formulations.

In geometry, a trapezoid () in North American English, or trapezium () in British English, is a quadrilateral that has at least one pair of parallel sides.

quadrilateral whose four sides can be grouped into two pairs of equal-length sides that are adjacent to each other

quadrilateral whose vertices can all fall on a single circle

quadrilateral whose sides are all tangent to a single circle interior to it

Rectangle with side lengths in the golden ratio

square whose sides have length 1

trapezoid symmetrical about an axis

REDIRECT Parallelogram Category:Types of quadrilaterals

type of shape

rhombus whose diagonal lengths are in the golden ratio

trapezoid whose four sides are all tangent to a circle within it

diagonally symmetrical quadrilateral with two opposing right angles

thumb|upright=0.9|An anti­parallelogram, Diagonals p and q are drawn using dotted lines, and height h is perpendicular to them.

quadrilateral in which the diagonals cross at right angles

quadrilateral with two equal sides perpendicular to the base

convex quadrilateral where the extensions of all four sides are tangent to a circle outside it

four points that determine six distinct lines

quadrilateral in which diagonals are of equal length

quadrilateral with three right angles

form of rhombus

cyclic quadrangle in which the products of the lengths of opposite sides are equal