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Given a convex quadrilateral, the following properties are equivalent, and each implies that the quadrilateral is a trapezoid: It has two adjacent angles that are supplementary, that is, they add up to 180 degrees. The angle between a side and a diagonal is equal to the angle between the opposite side and the same diagonal.
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 ...
Trapezium, plural trapezia, may refer to: Trapezium, in British and other forms of English, a trapezoid, a quadrilateral that has exactly one pair of parallel sides; Trapezium, in North American English, an irregular quadrilateral with no sides parallel; Trapezium (bone), a bone in the hand; Trapezium Cluster, a group of stars in the Orion Nebula
In spherical geometry, a spherical quadrilateral formed from four intersecting greater circles is cyclic if and only if the summations of the opposite angles are equal, i.e., α + γ = β + δ for consecutive angles α, β, γ, δ of the quadrilateral. [30] One direction of this theorem was proved by Anders Johan Lexell in 1782. [31]
The interior angle concept can be extended in a consistent way to crossed polygons such as star polygons by using the concept of directed angles.In general, the interior angle sum in degrees of any closed polygon, including crossed (self-intersecting) ones, is then given by 180(n–2k)°, where n is the number of vertices, and the strictly positive integer k is the number of total (360 ...
A handcuffed inmate whose fatal beating by correctional officers last year sparked outrage died by homicide, according to findings of an autopsy report a lawyer for the man's family shared Wednesday.
The base pairs form a parallelogram with half the area of the quadrilateral, A q, as the sum of the areas of the four large triangles, A l is 2 A q (each of the two pairs reconstructs the quadrilateral) while that of the small triangles, A s is a quarter of A l (half linear dimensions yields quarter area), and the area of the parallelogram is A ...
There are exactly 23 months between Jason and Travis Kelce: Jason was born on Nov. 5, 1987, and Travis arrived on Oct. 5, 1989. The two grew up in Cleveland Heights, Ohio, where their father Ed ...