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An equidiagonal quadrilateral | equidiagonal kite ( geometry ) | kite that maximizes the ratio of perimeter to diameter, inscribed in a Reuleaux triangle
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equidiagonal and quadrilateral
The diagonals of an isosceles trapezoid have the same length ; that is, every isosceles trapezoid is an equidiagonal quadrilateral.
equidiagonal and kite
* Among all quadrilaterals, the shape that has the greatest ratio of its perimeter to its diameter is an equidiagonal kite that can be inscribed into a Reuleaux triangle.
quadrilateral and |
Four central water courses define Charbagh | Char Bagh Garden's quadrilateral layout
quadrilateral and kite
In Euclidean geometry, a kite is a quadrilateral whose four sides can be grouped into two pairs of equal-length sides that are adjacent to each other.
In general, any quadrilateral with perpendicular diagonals, one of which is a line of symmetry, is a kite.
Every rhombus is a kite, and any quadrilateral that is both a kite and parallelogram is a rhombus.
When three steps are used to turn a 90 ° corner, the middle step is called a kite winder as a kite-shaped quadrilateral.
Any non-self-crossing quadrilateral with exactly one axis of symmetry must be either an isosceles trapezoid or a kite.
A square is a special case of a rhombus ( equal sides, opposite equal angles ), a kite ( two pairs of adjacent equal sides ), a parallelogram ( opposite sides parallel ), a quadrilateral or tetragon ( four-sided polygon ), and a rectangle ( opposite sides equal, right-angles ) and therefore has all the properties of all these shapes, namely:
quadrilateral and geometry
* Kite ( geometry ), a kite-shaped quadrilateral
< center > Lambert quadrilateral in hyperbolic geometry </ center >
The fourth angle of a Lambert quadrilateral is acute if the geometry is hyperbolic, a right angle if the geometry is Euclidean or obtuse if the geometry is elliptic.
The summit angles of a Saccheri quadrilateral are acute if the geometry is hyperbolic, right angles if the geometry is Euclidean and obtuse angles if the geometry is elliptic.
In Euclidean geometry, a parallelogram is a simple ( non self-intersecting ) quadrilateral with two pairs of parallel sides.
In Euclidean geometry, a rhombus (◊), plural rhombi or rhombuses, is a simple ( non self-intersecting ) quadrilateral whose four sides all have the same length.
In Euclidean geometry, Brahmagupta's formula finds the area of any cyclic quadrilateral ( one that can be inscribed in a circle ) given the lengths of the sides.
In Euclidean geometry, a cyclic quadrilateral or inscribed quadrilateral is a quadrilateral whose vertices all lie on a single circle.
* Euler centre and maltitudes of cyclic quadrilateral at Dynamic Geometry Sketches, interactive dynamic geometry sketch.
In Euclidean geometry, a convex quadrilateral with at least one pair of parallel sides ( see definition below ) is referred to as a trapezoid in American English and as a trapezium in English outside North America.
The close axiomatic study of Euclidean geometry led to the construction of the Lambert quadrilateral and the Saccheri quadrilateral.
* Kite ( geometry ), also known as a deltoid, a type of quadrilateral
In geometry, a square is a regular quadrilateral.
* Complete quadrilateral, in projective geometry, a configuration with 4 lines and 6 points
In Euclidean geometry, Ptolemy's theorem is a relation between the four sides and two diagonals of a cyclic quadrilateral ( a quadrilateral whose vertices lie on a common circle ).
quadrilateral and perimeter
* A square has a larger area than any other quadrilateral with the same perimeter.
quadrilateral and diameter
If now diameter AF is drawn bisecting DC so that DF and CF are sides c of an inscribed decagon, Ptolemy's Theorem can again be applied – this time to cyclic quadrilateral ADFC with diameter d as one of its diagonals:
The ancient geometers are not done yet, for if the fifth vertex of the pentagon is marked as E and FE and BF are joined ( with FE = BF = z ), then cyclic quadrilateral EFBA will be formed with diagonals length d ( diameter ) and b. Applying the ' Almagest ' theorem yet again:
quadrilateral and inscribed
It is a property of cyclic quadrilaterals ( and ultimately of inscribed angles ) that opposite angles of a quadrilateral sum to 180 °.
Consequently, in the case of an inscribed quadrilateral, θ = 90 °, whence the term
As a consequence of the theorem, opposite angles of cyclic quadrilaterals sum to 180 °; conversely, any quadrilateral for which this is true can be inscribed in a circle.
A quadrilateral ABCD with concyclic vertices is called a cyclic quadrilateral ; this happens if and only if ( the inscribed angle theorem ) which is true if and only if the opposite angles inside the quadrilateral are supplementary.
If both lines are not diameters, the we may extend the tangents drawn from each pole to produce a quadrilateral with the unit circle inscribed within it.
: In a quadrilateral, if the sum of the products of its two pairs of opposite sides is equal to the product of its diagonals, then the quadrilateral can be inscribed in a circle.
quadrilateral and triangle
A polygon is a generalization of a 3-sided triangle, a 4-sided quadrilateral, and so on to n sides.
The triangle, quadrilateral or quadrangle, and nonagon are exceptions.
A triangle may be regarded as a quadrilateral with one side of length zero.
From this perspective, as d approaches zero, a cyclic quadrilateral converges into a cyclic triangle ( all triangles are cyclic ), and Brahmagupta's formula simplifies to Heron's formula.
If also, the cyclic quadrilateral becomes a triangle and the formula is reduced to Heron's formula.
If the diagonals of a cyclic quadrilateral intersect at P, and the midpoints of the diagonals are M and N, then the anticenter of the quadrilateral is the orthocenter of triangle MNP.
The approximate area is the product of the halves of the sums of the sides and opposite sides of a triangle and a quadrilateral.
The two segments of the two diagonals are two sides in a triangle ; the base the quadrilateral is the base of the triangle.
Such a triangle has the same area as the quadrilateral and can be constructed from it by cutting and pasting.
The four brightest stars form a quadrilateral, and another three, a triangle north of them.
Each quadrilateral visible in the image consists of a pair of hyperbolic triangles ; each triangle is a fundamental domain of the modular group.
Any three of the lines of the quadrilateral form the sides of a triangle ; the orthocenters of the four triangles formed in this way lie on a second line, perpendicular to the one through the midpoints.
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