Concept
Rhombus
Related concepts (39)
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.
Parallelepiped
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. In Euclidean geometry, the four concepts—parallelepiped and cube in three dimensions, parallelogram and square in two dimensions—are defined, but in the context of a more general affine geometry, in which angles are not differentiated, only parallelograms and parallelepipeds exist.
Square
In Euclidean geometry, a square is a regular quadrilateral, which means that it has four equal sides and four equal angles (90-degree angles, π/2 radian angles, or right angles). It can also be defined as a rectangle with two equal-length adjacent sides. It is the only regular polygon whose internal angle, central angle, and external angle are all equal (90°), and whose diagonals are all equal in length. A square with vertices ABCD would be denoted .
Kite (geometry)
In Euclidean geometry, a kite is a quadrilateral with reflection symmetry across a diagonal. Because of this symmetry, a kite has two equal angles and two pairs of adjacent equal-length sides. Kites are also known as deltoids, but the word deltoid may also refer to a deltoid curve, an unrelated geometric object sometimes studied in connection with quadrilaterals. A kite may also be called a dart, particularly if it is not convex.
Rectangle
In Euclidean plane geometry, a rectangle is 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 occasionally used to refer to a non-square rectangle. A rectangle with vertices ABCD would be denoted as .
Cyclic quadrilateral
In Euclidean geometry, a cyclic quadrilateral or inscribed quadrilateral is a quadrilateral whose vertices all lie on a single circle. This circle is called the circumcircle or circumscribed circle, and the vertices are said to be concyclic. The center of the circle and its radius are called the circumcenter and the circumradius respectively. Other names for these quadrilaterals are concyclic quadrilateral and chordal quadrilateral, the latter since the sides of the quadrilateral are chords of the circumcircle.
Perimeter
A perimeter is a closed path that encompasses, surrounds, or outlines either a two dimensional shape or a one-dimensional length. The perimeter of a circle or an ellipse is called its circumference. Calculating the perimeter has several practical applications. A calculated perimeter is the length of fence required to surround a yard or garden. The perimeter of a wheel/circle (its circumference) describes how far it will roll in one revolution.
Quadrilateral
In geometry a quadrilateral is a four-sided polygon, having four edges (sides) and four corners (vertices). The word is derived from the Latin words quadri, a variant of four, and latus, meaning "side". It is also called a tetragon, derived from greek "tetra" meaning "four" and "gon" meaning "corner" or "angle", in analogy to other polygons (e.g. pentagon). Since "gon" means "angle", it is analogously called a quadrangle, or 4-angle. A quadrilateral with vertices , , and is sometimes denoted as .
Rhombic triacontahedron
In geometry, the rhombic triacontahedron, sometimes simply called the triacontahedron as it is the most common thirty-faced polyhedron, is a convex polyhedron with 30 rhombic faces. It has 60 edges and 32 vertices of two types. It is a Catalan solid, and the dual polyhedron of the icosidodecahedron. It is a zonohedron. The ratio of the long diagonal to the short diagonal of each face is exactly equal to the golden ratio, φ, so that the acute angles on each face measure 2 tan^−1(1/φ) = tan^−1(2), or approximately 63.
Cuboid
In geometry, a cuboid is a hexahedron, a six-faced solid. Its faces are quadrilaterals. Cuboid means "like a cube". A cuboid is like a cube in the sense that by adjusting the lengths of the edges or the angles between faces a cuboid can be transformed into a cube. In mathematical language a cuboid is a convex polyhedron whose polyhedral graph is the same as that of a cube. A special case of a cuboid is a rectangular cuboid, with six rectangles as faces. Its adjacent faces meet at right angles.