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The diagonals of a rhombus intersect at equal angles, while the diagonals of a rectangle are equal in length. The figure formed by joining the midpoints of the sides of a rhombus is a rectangle , and vice versa.
In Euclidean geometry, an equidiagonal quadrilateral is a convex quadrilateral whose two diagonals have equal length. Equidiagonal quadrilaterals were important in ancient Indian mathematics , where quadrilaterals were classified first according to whether they were equidiagonal and then into more specialized types.
A convex quadrilateral is a rectangle if and only if it is any one of the following: [5] [6]. a parallelogram with at least one right angle; a parallelogram with diagonals of equal length
Equidiagonal quadrilateral: the diagonals are of equal length. Bisect-diagonal quadrilateral: one diagonal bisects the other into equal lengths. Every dart and kite is bisect-diagonal. When both diagonals bisect another, it's a parallelogram. Ex-tangential quadrilateral: the four extensions of the sides are tangent to an excircle.
A quadrilateral is a square if and only if it is any one of the following: [2] [3] A rectangle with two adjacent equal sides; A rhombus with a right vertex angle; A rhombus with all angles equal; A parallelogram with one right vertex angle and two adjacent equal sides; A quadrilateral with four equal sides and four right angles
A kite is a quadrilateral with reflection symmetry across one of its diagonals. Equivalently, it is a quadrilateral whose four sides can be grouped into two pairs of adjacent equal-length sides. [1] [7] A kite can be constructed from the centers and crossing points of any two intersecting circles. [8]
Coxeter states that every zonogon (a 2m-gon whose opposite sides are parallel and of equal length) can be dissected into () or 1 / 2 m(m − 1) parallelograms. These tilings are contained as subsets of vertices, edges and faces in orthogonal projections m -cubes . [ 7 ]
Any non-self-crossing quadrilateral with exactly one axis of symmetry must be either an isosceles trapezoid or a kite. [5] However, if crossings are allowed, the set of symmetric quadrilaterals must be expanded to include also the crossed isosceles trapezoids, crossed quadrilaterals in which the crossed sides are of equal length and the other sides are parallel, and the antiparallelograms ...