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  2. Kite (geometry) - Wikipedia

    en.wikipedia.org/wiki/Kite_(geometry)

    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 ...

  3. Isosceles trapezoid - Wikipedia

    en.wikipedia.org/wiki/Isosceles_trapezoid

    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 ...

  4. Cyclic quadrilateral - Wikipedia

    en.wikipedia.org/wiki/Cyclic_quadrilateral

    The first of these theorems is the spherical analogue of a plane theorem, and the second theorem is its dual, that is, the result of interchanging great circles and their poles. [32] Kiper et al. [ 33 ] proved a converse of the theorem: If the summations of the opposite sides are equal in a spherical quadrilateral, then there exists an ...

  5. Orthodiagonal quadrilateral - Wikipedia

    en.wikipedia.org/wiki/Orthodiagonal_quadrilateral

    A square is a limiting case of both a kite and a rhombus. Orthodiagonal equidiagonal quadrilaterals in which the diagonals are at least as long as all of the quadrilateral's sides have the maximum area for their diameter among all quadrilaterals, solving the n = 4 case of the biggest little polygon problem. The square is one such quadrilateral ...

  6. Quadrilateral - Wikipedia

    en.wikipedia.org/wiki/Quadrilateral

    Tangential trapezoid: a trapezoid where the four sides are tangents to an inscribed circle. Cyclic quadrilateral: the four vertices lie on a circumscribed circle. A convex quadrilateral is cyclic if and only if opposite angles sum to 180°. Right kite: a kite with two opposite right angles. It is a type of cyclic quadrilateral.

  7. Right kite - Wikipedia

    en.wikipedia.org/wiki/Right_kite

    In Euclidean geometry, a right kite is a kite (a quadrilateral whose four sides can be grouped into two pairs of equal-length sides that are adjacent to each other) that can be inscribed in a circle. [1] That is, it is a kite with a circumcircle (i.e., a cyclic kite). Thus the right kite is a convex quadrilateral and has two opposite right ...

  8. Equidiagonal quadrilateral - Wikipedia

    en.wikipedia.org/wiki/Equidiagonal_quadrilateral

    A convex quadrilateral is equidiagonal if and only if its Varignon parallelogram, the parallelogram formed by the midpoints of its sides, is a rhombus.An equivalent condition is that the bimedians of the quadrilateral (the diagonals of the Varignon parallelogram) are perpendicular.

  9. Tangential trapezoid - Wikipedia

    en.wikipedia.org/wiki/Tangential_trapezoid

    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.)

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