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The centers of four squares all constructed either internally or externally on the sides of a parallelogram are the vertices of a square. [8] If two lines parallel to sides of a parallelogram are constructed concurrent to a diagonal, then the parallelograms formed on opposite sides of that diagonal are equal in area. [8]
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).
In any quadrilateral, the four edge midpoints form a parallelogram, the Varignon parallelogram, whose sides are parallel to the diagonals and half their length.It follows that, in an equidiagonal and orthodiagonal quadrilateral, the sides of the Varignon parallelogram are equal-length and perpendicular; that is, it is a square.
Denotes square root and is read as the square root of. Rarely used in modern mathematics without a horizontal bar delimiting the width of its argument (see the next item). For example, √2. √ (radical symbol) 1. Denotes square root and is read as the square root of. For example, +. 2.
Definitions Images Parallelepiped: A polyhedron with six faces , each of which is a parallelogram; A hexahedron with three pairs of parallel faces; A prism of which the base is a parallelogram; Rhombohedron: A parallelepiped where all edges are the same length; A cube, except that its faces are not squares but rhombi; Cuboid
A square is said to be inscribed in a curve whenever all four vertices of the square lie on the curve. It is an unsolved problem in mathematics, the inscribed square problem, whether every simple closed curve has an inscribed square. Some cases of this problem are known to be true; for instance, it is true for every smooth curve. [61]
In geometry, a parallelepiped is a three-dimensional figure formed by six parallelograms (the term rhomboid is also sometimes used with this meaning). By analogy, it relates to a parallelogram just as a cube relates to a square. [a] Three equivalent definitions of parallelepiped are a hexahedron with three pairs of parallel faces,
A root of degree 2 is called a square root and a root of degree 3, a cube root. Roots of higher degree are referred to by using ordinal numbers, as in fourth root, twentieth root, etc. For example: 2 is a square root of 4, since 2 2 = 4. −2 is also a square root of 4, since (−2) 2 = 4.