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The rhombus has a square as a special case, and is a special case of a kite and parallelogram. In plane Euclidean geometry , a rhombus ( pl. : rhombi or rhombuses ) is a quadrilateral whose four sides all have the same length.
A square can also be defined as a parallelogram with equal diagonals that bisect the angles. If a figure is both a rectangle (right angles) and a rhombus (equal edge lengths), then it is a square. A square has a larger area than any other quadrilateral with the same perimeter. [7]
The definition of lozenge is not strictly fixed, and the word is sometimes used simply as a synonym (from Old French losenge) for rhombus. Most often, though, lozenge refers to a thin rhombus—a rhombus with two acute and two obtuse angles, especially one with acute angles of 45°. [ 2 ]
A parallelogram has rotational symmetry of order 2 (through 180°) (or order 4 if a square). If it also has exactly two lines of reflectional symmetry then it must be a rhombus or an oblong (a non-square rectangle). If it has four lines of reflectional symmetry, it is a square.
A square is a limiting case of both a kite and a rhombus. Orthodiagonal equidiagonal quadrilaterals in which the diagonals are at least as long as all of the quadrilateral's sides have the maximum area for their diameter among all quadrilaterals, solving the n = 4 case of the biggest little polygon problem.
Additionally, if a convex kite is not a rhombus, there is a circle outside the kite that is tangent to the extensions of the four sides; therefore, every convex kite that is not a rhombus is an ex-tangential quadrilateral. The convex kites that are not rhombi are exactly the quadrilaterals that are both tangential and ex-tangential. [16]
In recent weeks, payment-processing specialist Square (NYSE:SQ) has incurred notable volatility. Most likely, the weakness in Square stock is due to broader concerns impacting the major indices ...
An equivalent condition is that opposite sides are parallel (a square is a parallelogram), and that the diagonals perpendicularly bisect each other and are of equal length. 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).