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height/altitude: trapezoid/trapezium with opposing triangles , formed by the diagonals. 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.
For more, see Trapezoid § Trapezium vs Trapezoid.) Trapezium (UK) or trapezoid (US): at least one pair of opposite sides are parallel. Trapezia (UK) and trapezoids (US) include parallelograms. Isosceles trapezium (UK) or isosceles trapezoid (US): one pair of opposite sides are parallel and the base angles are equal in measure. Alternative ...
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 ...
In calculus, the trapezoidal rule (also known as the trapezoid rule or trapezium rule) [a] is a technique for numerical integration, i.e., approximating the definite integral: (). The trapezoidal rule works by approximating the region under the graph of the function f ( x ) {\displaystyle f(x)} as a trapezoid and calculating its area.
The vertices of every triangle fall on a circle called the circumcircle. (Because of this, some authors define "concyclic" only in the context of four or more points on a circle.) [2] Several other sets of points defined from a triangle are also concyclic, with different circles; see Nine-point circle [3] and Lester's theorem.
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
The formula for the area of a trapezoid can be simplified using Pitot's theorem to get a formula for the area of a tangential trapezoid. If the bases have lengths a, b, and any one of the other two sides has length c, then the area K is given by the formula [2] (This formula can be used only in cases where the bases are parallel.)
In mathematics, a property is any characteristic that applies to a given set. [1] Rigorously, a property p defined for all elements of a set X is usually defined as a function p: X → {true, false}, that is true whenever the property holds; or, equivalently, as the subset of X for which p holds; i.e. the set {x | p(x) = true}; p is its indicator function.