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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 obtuse trapezoid on the other hand has one acute and one obtuse angle on each base. An isosceles trapezoid is a trapezoid where the base angles have the same measure. As a consequence the two legs are also of equal length and it has reflection symmetry. This is possible for acute trapezoids or right trapezoids (as rectangles).
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 ...
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 ...
Triangles with reflection symmetry are isosceles. Quadrilaterals with reflection symmetry are kites, (concave) deltoids, rhombi, [2] and isosceles trapezoids.All even-sided polygons have two simple reflective forms, one with lines of reflections through vertices, and one through edges.
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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The cyclic equidiagonal quadrilaterals are exactly the isosceles trapezoids. There is a duality between equidiagonal quadrilaterals and orthodiagonal quadrilaterals : a quadrilateral is equidiagonal if and only if its Varignon parallelogram is orthodiagonal (a rhombus), and the quadrilateral is orthodiagonal if and only if its Varignon ...