triangle is a quadrilateral with 2 pairs of equal sides and 2 pairs of opposite angles that are equal.
quadrilateral with 2 pairs of equal sides and 2 pairs of opposite angles that are equal?
triangle
a square is a special case of a rhombus (equal sides, opposite equal angles), a kite (two pairs of adjacent equal sides), a trapezoid (one pair of opposite sides parallel), a parallelogram (all opposite sides parallel), a quadrilateral or tetragon (four-sided polygon), and a rectangle (opposite sides equal, right-angles) and therefore has all the properties of all these shapes, namely:





















































bullet::::- the diagonals of a square bisect each other and meet at 90°





















































bullet::::- the diagonals of a square bisect its angles.





















































bullet::::- opposite sides of a square are both parallel and equal in length.
square
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. one direction of this theorem was proved by i. a. lexell in 1786. lexell showed that in a spherical quadrilateral inscribed in a small circle of a sphere the sums of opposite angles are equal, and that in the circumscribed quadrilateral the sums of opposite sides are equal. 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. kiper et al. proved a converse of the theorem: if the summations of the opposite sides are equal in a spherical quadrilateral, then there exists an inscribing circle for this quadrilateral.
cyclic quadrilateral