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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 ...
An isosceles trapezoid is a trapezoid where the base angles have the same measure. ... Given a convex quadrilateral, the following properties are equivalent, and each ...
A kite and its dual isosceles trapezoid. Kites and isosceles trapezoids are dual to each other, meaning that there is a correspondence between them that reverses the dimension of their parts, taking vertices to sides and sides to vertices. From any kite, the inscribed circle is tangent to its four sides at the four vertices of an isosceles ...
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 definitions are a quadrilateral with an axis of symmetry bisecting one pair of opposite sides, or a trapezoid with diagonals of equal length.
A triangle that is not isosceles (having three unequal sides) is called scalene. [3] "Isosceles" is made from the Greek roots "isos" (equal) and "skelos" (leg). The same word is used, for instance, for isosceles trapezoids, trapezoids with two equal sides, [4] and for isosceles sets, sets of points every three of which form an isosceles ...
Every isosceles tangential trapezoid is bicentric. An isosceles tangential trapezoid is a tangential trapezoid where the legs are equal. Since an isosceles trapezoid is cyclic, an isosceles tangential trapezoid is a bicentric quadrilateral. That is, it has both an incircle and a circumcircle. If the bases are a, b, then the inradius is given by [7]
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[6] [7] The convex hull of an antiparallelogram is an isosceles trapezoid, and every antiparallelogram may be formed from an isosceles trapezoid (or its special cases, the rectangles and squares) by replacing two parallel sides by the two diagonals of the trapezoid. [4]